{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T18:54:49Z","timestamp":1767984889790,"version":"3.49.0"},"reference-count":127,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2012,5,2]],"date-time":"2012-05-02T00:00:00Z","timestamp":1335916800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2012,10]]},"DOI":"10.1007\/s00332-012-9127-4","type":"journal-article","created":{"date-parts":[[2012,5,1]],"date-time":"2012-05-01T16:47:34Z","timestamp":1335890854000},"page":"763-811","source":"Crossref","is-referenced-by-count":56,"title":["Numerical Study of Blow up and Stability of Solutions of Generalized Kadomtsev\u2013Petviashvili Equations"],"prefix":"10.1007","volume":"22","author":[{"given":"C.","family":"Klein","sequence":"first","affiliation":[]},{"given":"J.-C.","family":"Saut","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"issue":"2","key":"9127_CR1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0375-9601(83)90208-6","volume":"94","author":"M.J. Ablowitz","year":"1983","unstructured":"Ablowitz, M.J., Fokas, A.: On the inverse scattering and direct linearizing transforms for the Kadomtsev\u2013Petviashvili equation. Phys. Lett. A 94(2), 67\u201370 (1983)","journal-title":"Phys. Lett. A"},{"key":"9127_CR2","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1017\/S0022112079000835","volume":"92","author":"M.J. Ablowitz","year":"1979","unstructured":"Ablowitz, M.J., Segur, H.: On the evolution of packets of water waves. J. Fluid Mech. 92, 691\u2013715 (1979)","journal-title":"J. Fluid Mech."},{"key":"9127_CR3","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1111\/1467-9590.00220","volume":"109","author":"M.J. Ablowitz","year":"2002","unstructured":"Ablowitz, M.J., Villarroel, J.: The Cauchy problem for the Kadomtsev\u2013Petviashvili II equation with nondecaying data along a line. Stud. Appl. Math. 109, 151\u2013162 (2002)","journal-title":"Stud. Appl. Math."},{"key":"9127_CR4","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1088\/0951-7715\/17\/5\/015","volume":"17","author":"M.J. Ablowitz","year":"2004","unstructured":"Ablowitz, M.J., Villarroel, J.: The Cauchy problem for the Kadomtsev\u2013Petviashvili II equation with data that do not decay along a line. Nonlinearity 17, 1843\u20131866 (2004)","journal-title":"Nonlinearity"},{"issue":"5","key":"9127_CR5","first-page":"963","volume":"61","author":"L.A. Abramyan","year":"1985","unstructured":"Abramyan, L.A., Stepanyants, Y.A.: The structure of two-dimensional solitons in media with anomalously small dispersion. Sov. Phys. JETP 61(5), 963\u2013966 (1985)","journal-title":"Sov. Phys. JETP"},{"key":"9127_CR6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0375-9601(96)00921-8","volume":"226","author":"J.C. Alexander","year":"1997","unstructured":"Alexander, J.C., Pego, R.L., Sachs, R.L.: On the transverse instability of solitary waves in the Kadomtsev\u2013Petviashvili equation. Phys. Lett. A 226, 187\u2013192 (1997)","journal-title":"Phys. Lett. A"},{"issue":"2","key":"9127_CR7","doi-asserted-by":"crossref","first-page":"263","DOI":"10.4310\/MAA.2000.v7.n2.a1","volume":"7","author":"D. Alterman","year":"1999","unstructured":"Alterman, D., Rauch, J.: The linear diffractive pulse equation. Methods Appl. Anal. 7(2), 263\u2013274 (1999)","journal-title":"Methods Appl. Anal."},{"issue":"2","key":"9127_CR8","first-page":"137","volume":"12","author":"M. Ben-Artzi","year":"1999","unstructured":"Ben-Artzi, M., Saut, J.-C.: Uniform decay estimates for a class of oscillatory integrals and applications. Differ. Integral Equ. 12(2), 137\u2013145 (1999)","journal-title":"Differ. Integral Equ."},{"issue":"5\u20136","key":"9127_CR9","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1081\/PDE-120004892","volume":"27","author":"Y. Ben-Youssef","year":"2002","unstructured":"Ben-Youssef, Y., Lannes, D.: The long wave limit for a general class of 2D quasilinear hyperbolic problems. Commun. Partial Differ. Equ. 27(5\u20136), 979\u20131020 (2002)","journal-title":"Commun. Partial Differ. Equ."},{"key":"9127_CR10","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1098\/rsta.1972.0032","volume":"272","author":"T.B. Benjamin","year":"1972","unstructured":"Benjamin, T.B., Bona, J.L., Mahony, J.J.: Models equations for long waves in nonlinear dispersive systems. Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci. 272, 47\u201378 (1972)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci."},{"key":"9127_CR11","volume-title":"Integral Representations of Functions and Imbedding Theorems","author":"O.V. Besov","year":"1978","unstructured":"Besov, O.V., Il\u2019in, V.P., Nikolskii, S.M.: Integral Representations of Functions and Imbedding Theorems, vol.\u00a0I. Wiley, New York (1978)"},{"issue":"3","key":"9127_CR12","doi-asserted-by":"crossref","first-page":"241","DOI":"10.4310\/DPDE.2008.v5.n3.a3","volume":"5","author":"F. B\u00e9thuel","year":"2008","unstructured":"B\u00e9thuel, F., Gravejat, P., Saut, J.-C.: On the KP I transonic limit of two-dimensional Gross\u2013Pitaevskii travelling waves. Dyn. Partial Differ. Equ. 5(3), 241\u2013280 (2008)","journal-title":"Dyn. Partial Differ. Equ."},{"issue":"1","key":"9127_CR13","first-page":"1","volume":"7","author":"J.L. Bona","year":"2002","unstructured":"Bona, J.L., Liu, Y.: Instability of solitary- wave solutions of the 3-dimensional Kadomtsev\u2013Petviashvili equation. Adv. Differ. Equ. 7(1), 1\u201323 (2002)","journal-title":"Adv. Differ. Equ."},{"key":"9127_CR14","first-page":"235","volume":"20","author":"J.L. Bona","year":"1983","unstructured":"Bona, J.L., Pritchard, W.G., Scott, L.R.: A comparison of solutions of two model equations for long waves. Lect. Appl. Math. 20, 235\u2013267 (1983)","journal-title":"Lect. Appl. Math."},{"issue":"2","key":"9127_CR15","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1006\/jdeq.2002.4171","volume":"185","author":"J.L. Bona","year":"2002","unstructured":"Bona, J.L., Liu, Y., Tom, M.: The Cauchy problem and stability of solitary wave solutions for RLW-KP type equations. J. Differ. Equ. 185(2), 437\u2013482 (2002)","journal-title":"J. Differ. Equ."},{"issue":"4","key":"9127_CR16","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF01896259","volume":"3","author":"J. Bourgain","year":"1993","unstructured":"Bourgain, J.: On the Cauchy problem for the Kadomtsev\u2013Petviashvili equation. Geom. Funct. Anal. 3(4), 315\u2013341 (1993)","journal-title":"Geom. Funct. Anal."},{"key":"9127_CR17","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1515\/ans-2010-0209","volume":"10","author":"J. Chen","year":"2010","unstructured":"Chen, J., Liu, Y.: Solutions of the generalized rotation-modifed Kadomtsev\u2013Petviashvili equation. Adv. Nonlinear Stud. 10, 413\u2013432 (2010)","journal-title":"Adv. Nonlinear Stud."},{"issue":"1","key":"9127_CR18","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1137\/080738994","volume":"42","author":"D. Chiron","year":"2010","unstructured":"Chiron, D., Rousset, F.: The KdV\/KP limit of the Nonlinear Schr\u00f6dinger equation. SIAM J. Math. Anal. 42(1), 64\u201396 (2010)","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"9127_CR19","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1006\/jcph.2002.6995","volume":"176","author":"S.M. Cox","year":"2002","unstructured":"Cox, S.M., Matthews, P.C.: Exponential time differencing for stiff systems. J. Comput. Phys. 176(2), 430\u2013455 (2002)","journal-title":"J. Comput. Phys."},{"key":"9127_CR20","unstructured":"Darwich, M.: On the well-posedness of Kadomtsev\u2013Petviashvili\u2013Burgers I equation, arXiv:1111.1518v1 [math.AP]. 7 Nov 2011"},{"key":"9127_CR21","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s00208-003-0498-6","volume":"328","author":"A. Bouard de","year":"2004","unstructured":"de Bouard, A., Martel, Y.: Nonexistence of L 2-compact solutions of the Kadomtsev\u2013Petviashvili II equation. Math. Ann. 328, 525\u2013544 (2004)","journal-title":"Math. Ann."},{"key":"9127_CR22","series-title":"Contemporary Mathematics","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1090\/conm\/200\/02510","volume-title":"Mathematical Problems in the Theory of Water Waves","author":"A. Bouard de","year":"1996","unstructured":"de Bouard, A., Saut, J.-C.: Remarks on the stability of the generalized Kadomtsev\u2013Petviashvili solitary waves. In: Dias, F., Ghidaglia, J.-M., Saut, J.-C. (eds.) Mathematical Problems in the Theory of Water Waves. Contemporary Mathematics, vol. 200, pp. 75\u201384. AMS, Providence (1996)"},{"issue":"2","key":"9127_CR23","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0294-1449(97)80145-X","volume":"14","author":"A. Bouard de","year":"1997","unstructured":"de Bouard, A., Saut, J.-C.: Solitary waves of the generalized KP equations. Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire 14(2), 211\u2013236 (1997a)","journal-title":"Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"issue":"5","key":"9127_CR24","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1137\/S0036141096297662","volume":"28","author":"A. Bouard de","year":"1997","unstructured":"de Bouard, A., Saut, J.-C.: Symmetry and decay of the generalized Kadomtsev\u2013Petviashvili solitary waves. SIAM J. Math. Anal. 28(5), 104\u20131085 (1997b)","journal-title":"SIAM J. Math. Anal."},{"key":"9127_CR25","first-page":"753","volume":"19","author":"V.S. Druyma","year":"1974","unstructured":"Druyma, V.S.: On the analytical solution of the two-dimensional Korteweg\u2013de Vries equation. JETP Lett. 19, 753\u2013757 (1974)","journal-title":"JETP Lett."},{"key":"9127_CR26","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1088\/0951-7715\/24\/3\/006","volume":"24","author":"A. Esfahani","year":"2011","unstructured":"Esfahani, A.: Instability of solitary waves of the generalized higher-order KP equation. Nonlinearity 24, 833\u2013846 (2011)","journal-title":"Nonlinearity"},{"key":"9127_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0266-5611\/25\/12\/123007","volume":"25","author":"A.S. Fokas","year":"2009","unstructured":"Fokas, A.S.: Lax pairs: a novel type of separability. Inverse Probl. 25, 1\u201344 (2009)","journal-title":"Inverse Probl."},{"key":"9127_CR28","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1088\/0951-7715\/16\/2\/323","volume":"16","author":"A.S. Fokas","year":"2003","unstructured":"Fokas, A.S., Pogrebkov, A.K.: Inverse scattering transform for the KP I equation on the background of a one-line soliton. Nonlinearity 16, 771\u2013783 (2003)","journal-title":"Nonlinearity"},{"key":"9127_CR29","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1017\/S0305004198002850","volume":"125","author":"A.S. Fokas","year":"1999","unstructured":"Fokas, A.S., Sung, L.Y.: The inverse spectral method for the KP I equation without the zero mass constraint. Math. Proc. Camb. Philos. Soc. 125, 113\u2013138 (1999)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"4","key":"9127_CR30","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1017\/S0308210500001165","volume":"131","author":"T. Gallay","year":"2001","unstructured":"Gallay, T., Schneider, G.: KP description of unidirectional long waves. The model case. Proc. R. Soc. Edinb., Sect. A 131(4), 885\u2013898 (2001)","journal-title":"Proc. R. Soc. Edinb., Sect. A"},{"key":"9127_CR31","first-page":"163","volume-title":"S\u00e9m. N. Bourbaki, exp. No. 706","author":"J. Ginibre","year":"1994\u20131995","unstructured":"Ginibre, J.: Le\u00a0probl\u00e8me de\u00a0Cauchy pour des EDP semi lin\u00e9aires p\u00e9riodiques en variables d\u2019espace. In: S\u00e9m. N. Bourbaki, exp. No. 706, pp. 163\u2013187 (1994\u20131995)"},{"issue":"3","key":"9127_CR32","doi-asserted-by":"crossref","first-page":"835","DOI":"10.3934\/dcds.2008.21.835","volume":"21","author":"P. Gravejat","year":"2008","unstructured":"Gravejat, P.: Asymptotics of the solitary waves for the generalised Kadomtsev\u2013Petviashvili equations. Discrete Contin. Dyn. Syst. 21(3), 835\u2013882 (2008)","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"9127_CR33","first-page":"1","volume":"82","author":"A. Gr\u00fcnrock","year":"2009","unstructured":"Gr\u00fcnrock, A.: On the Cauchy problem for generalized Kadomtsev\u2013Petviashvili (KP II) equations. Electron. J. Differ. Equ. 82, 1\u20139 (2009)","journal-title":"Electron. J. Differ. Equ."},{"issue":"6","key":"9127_CR34","doi-asserted-by":"crossref","first-page":"2335","DOI":"10.1016\/j.anihpc.2009.04.002","volume":"26","author":"A. Gr\u00fcnrock","year":"2009","unstructured":"Gr\u00fcnrock, A., Panthee, M., Drumond Silva, J.: On KP II equations on cylinders. Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire 26(6), 2335\u20132358 (2009)","journal-title":"Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"key":"9127_CR35","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1016\/j.matpur.2010.03.012","volume":"94","author":"Z. Guo","year":"2010","unstructured":"Guo, Z., Peng, L., Wang, B.: On the local regularity of the KP I equation in anisotropic Sobolev spaces. J.\u00a0Math. Pures Appl. 94, 414\u2013432 (2010)","journal-title":"J.\u00a0Math. Pures Appl."},{"issue":"12","key":"9127_CR36","doi-asserted-by":"crossref","first-page":"6555","DOI":"10.1090\/S0002-9947-08-04515-7","volume":"360","author":"M. Hadac","year":"2008","unstructured":"Hadac, M.: Well-posedness for the Kadomtsev\u2013Petviashvili II equation and generalisations. Trans. Am. Math. Soc. 360(12), 6555\u20136572 (2008)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"9127_CR37","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.anihpc.2008.04.002","volume":"26","author":"M. Hadac","year":"2009","unstructured":"Hadac, M., Herr, S., Koch, H.: Well-posedness and scattering for the KP II equation in a critical space. Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire 26(3), 917\u2013941 (2009)","journal-title":"Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"issue":"5","key":"9127_CR38","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.4208\/cicp.2009.v6.p1022","volume":"6","author":"F. Hamidouche","year":"2009","unstructured":"Hamidouche, F., Mammeri, Y., Mefire, S.: Numerical study of the solutions of the 3D generalized Kadomtsev\u2013Petvisahvili equations for long times. Commun. Comput. Phys. 6(5), 1022\u20131062 (2009)","journal-title":"Commun. Comput. Phys."},{"key":"9127_CR39","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1111\/j.1467-9590.2010.00501.x","volume":"126","author":"M. Haragus","year":"2011","unstructured":"Haragus, M.: Transverse spectral stability of small periodic traveling waves for the KP equation. Stud. Appl. Math. 126, 157\u2013185 (2011)","journal-title":"Stud. Appl. Math."},{"key":"9127_CR40","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0764-4442(99)80126-8","volume":"328","author":"M. Haragus","year":"1999","unstructured":"Haragus, M., Pego, R.L.: Travelling waves of the KP equations with transverse modulations. C. R. Acad. Sci. Paris S\u00e9r. I 328, 227\u2013232 (1999)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I"},{"key":"9127_CR41","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s002200050569","volume":"201","author":"N. Hayashi","year":"1999","unstructured":"Hayashi, N., Naumkin, P., Saut, J.-C.: Asymptotics for large time of global solutions to the generalized Kadomtsev\u2013Petviashvili equation. Commun. Math. Phys. 201, 577\u2013590 (1999)","journal-title":"Commun. Math. Phys."},{"key":"9127_CR42","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1017\/S0962492910000048","volume":"19","author":"M. Hochbruck","year":"2010","unstructured":"Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numer. 19, 209\u2013286 (2010)","journal-title":"Acta Numer."},{"key":"9127_CR43","doi-asserted-by":"crossref","first-page":"3183","DOI":"10.1103\/PhysRevE.51.3183","volume":"51","author":"E. Infeld","year":"1995","unstructured":"Infeld, E., Senatorski, A., Skorupski, A.A.: Numerical simulations of Kadomtsev\u2013Petviashvili soliton interactions. Phys. Rev. E 51, 3183\u20133191 (1995)","journal-title":"Phys. Rev. E"},{"issue":"2021","key":"9127_CR44","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1098\/rspa.2001.0937","volume":"458","author":"E. Infeld","year":"2002","unstructured":"Infeld, E., Skorupski, A.A., Rowlands, G.: Instabilities and oscillations of one- and two-dimensional Kadomtsev\u2013Petviashvili waves and solitons. II. Linear to nonlinear analysis. Proc. - Royal Soc., Math. Phys. Eng. Sci. 458(2021), 1231\u20131244 (2002)","journal-title":"Proc. - Royal Soc., Math. Phys. Eng. Sci."},{"key":"9127_CR45","first-page":"181","volume":"163","author":"A. Ionescu","year":"2007","unstructured":"Ionescu, A., Kenig, C.: Local and global well-posedness of periodic KP I equations. Ann. Math. Stud. 163, 181\u2013211 (2007)","journal-title":"Ann. Math. Stud."},{"issue":"2","key":"9127_CR46","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s00222-008-0115-0","volume":"173","author":"A.D. Ionescu","year":"2008","unstructured":"Ionescu, A.D., Kenig, C., Tataru, D.: Global well-posedness of the initial value problem for the KP I equation in the energy space. Invent. Math. 173(2), 265\u2013304 (2008)","journal-title":"Invent. Math."},{"key":"9127_CR47","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1017\/S0308210500021740","volume":"128","author":"R.J. I\u00f3rio Jr.","year":"1998","unstructured":"I\u00f3rio, R.J. Jr., Nunes, W.V.L.: On equations of KP-type. Proc. R. Soc. Edinb. 128, 725\u2013743 (1998)","journal-title":"Proc. R. Soc. Edinb."},{"key":"9127_CR48","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1081\/PDE-100002387","volume":"26","author":"P. Isaza","year":"2001","unstructured":"Isaza, P., Mejia, J.: Local and global Cauchy problems for the Kadomtsev\u2013Petviashvili (KP-II) equation in Sobolev spaces of negative indices. Commun. Partial Differ. Equ. 26, 1027\u20131057 (2001)","journal-title":"Commun. Partial Differ. Equ."},{"key":"9127_CR49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jde.2004.10.002","volume":"220","author":"P. Isaza","year":"2006","unstructured":"Isaza, P., Mejia, J.: A smoothing effect and polynomial growth of the Sobolev norms for the KP II equation. J. Differ. Equ. 220, 1\u201317 (2006)","journal-title":"J. Differ. Equ."},{"issue":"4","key":"9127_CR50","doi-asserted-by":"crossref","first-page":"887","DOI":"10.3934\/cpaa.2006.5.887","volume":"5","author":"P. Isaza","year":"2006","unstructured":"Isaza, P., Lopez, J., Mejia, J.: Cauchy problem for the fifth order Kadomtsev\u2013Petviashvili (KP II) equation. Commun. Pure Appl. Anal. 5(4), 887\u2013905 (2006)","journal-title":"Commun. Pure Appl. Anal."},{"key":"9127_CR51","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1080\/03605300500530461","volume":"32","author":"P. Isaza","year":"2007","unstructured":"Isaza, P., Lopez, J., Mejia, J.: The Cauchy problem for the Kadomsteev\u2013Petviashvili (KP II) equation in thee space dimensions. Commun. Partial Differ. Equ. 32, 611\u2013641 (2007)","journal-title":"Commun. Partial Differ. Equ."},{"issue":"6","key":"9127_CR52","doi-asserted-by":"crossref","first-page":"2681","DOI":"10.1137\/090770758","volume":"42","author":"M. Johnson","year":"2010","unstructured":"Johnson, M., Zumbrun, K.: Transverse instability of periodic waves in the generalized Kadomtsev\u2013Petviashvili equation. SIAM J. Math. Anal. 42(6), 2681\u20132702 (2010)","journal-title":"SIAM J. Math. Anal."},{"key":"9127_CR53","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1088\/0305-4470\/15\/8\/036","volume":"15","author":"C.A. Jones","year":"1982","unstructured":"Jones, C.A., Roberts, P.H.: Motions in a Bose condensate, IV: Axisymmetric solitary waves. J. Phys. A, Math. Gen. 15, 2599\u20132619 (1982)","journal-title":"J. Phys. A, Math. Gen."},{"key":"9127_CR54","first-page":"539","volume":"15","author":"B.B. Kadomtsev","year":"1970","unstructured":"Kadomtsev, B.B., Petviashvili, V.I.: On the stability of solitary waves in weakly dispersing media. Sov. Phys. Dokl. 15, 539\u2013541 (1970)","journal-title":"Sov. Phys. Dokl."},{"key":"9127_CR55","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0375-9601(91)90750-3","volume":"154","author":"V.I. Karpman","year":"1991","unstructured":"Karpman, V.I., Belashov, V.Y.U.: Dynamics of two-dimensional solitons in weakly dispersing media. Phys. Rev. Lett. A 154, 131\u2013139 (1991a)","journal-title":"Phys. Rev. Lett. A"},{"key":"9127_CR56","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/0375-9601(91)90751-S","volume":"154","author":"V.I. Karpman","year":"1991","unstructured":"Karpman, V.I., Belashov, V.Y.U.: Evolution of three-dimensional pulses in weakly dispersive media. Phys. Rev. Lett. A 154, 140\u2013144 (1991b)","journal-title":"Phys. Rev. Lett. A"},{"key":"9127_CR57","series-title":"Adv. Math. Suppl. Stud.","first-page":"93","volume-title":"Studies in Applied Mathematics","author":"T. Kato","year":"1983","unstructured":"Kato, T.: On the Cauchy problem for the (generalized) Korteweg\u2013de Vries equations. In: Studies in Applied Mathematics. Adv. Math. Suppl. Stud., vol.\u00a08, pp.\u00a093\u2013128 (1983)"},{"issue":"2\u20133","key":"9127_CR58","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.physleta.2003.11.021","volume":"320","author":"D. Kaya","year":"2003","unstructured":"Kaya, D., Salah, E.M.: Numerical soliton-like solutions of the potential Kadomtsev\u2013Petviashvili equation by the decomposition method. Phys. Lett. A 320(2\u20133), 192\u2013199 (2003)","journal-title":"Phys. Lett. A"},{"key":"9127_CR59","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1016\/j.anihpc.2003.12.002","volume":"21","author":"C. Kenig","year":"2004","unstructured":"Kenig, C.: On the local and global well-posedness for the KP-I equation. Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire 21, 827\u2013838 (2004)","journal-title":"Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"key":"9127_CR60","first-page":"2447","volume":"358","author":"C. Kenig","year":"2006","unstructured":"Kenig, C., Martel, Y.: Global well-posedness in the energy space for a modified KP II equation via the Miura transform. Tamsui Oxf. J. Manag. Sci. 358, 2447\u20132488 (2006)","journal-title":"Tamsui Oxf. J. Manag. Sci."},{"key":"9127_CR61","first-page":"111","volume":"18","author":"C. Kenig","year":"2005","unstructured":"Kenig, C., Ziegler, S.: Local well-posedness for modified Kadomtsev\u2013Petviashvili equations. Differ. Integral Equ. 18, 111\u2013146 (2005a)","journal-title":"Differ. Integral Equ."},{"issue":"1","key":"9127_CR62","doi-asserted-by":"crossref","first-page":"45","DOI":"10.3934\/cpaa.2005.4.45","volume":"4","author":"C. Kenig","year":"2005","unstructured":"Kenig, C., Ziegler, S.: Maximal function estimates with applications to a modified KP equation. Commun. Pure Appl. Anal. 4(1), 45\u201391 (2005b)","journal-title":"Commun. Pure Appl. Anal."},{"key":"9127_CR63","first-page":"116","volume":"29","author":"C. Klein","year":"2008","unstructured":"Klein, C.: Fourth order time-stepping for low dispersion Korteweg\u2013de Vries and nonlinear Schr\u00f6dinger equation. Electron. Trans. Numer. Anal. 29, 116\u2013135 (2008)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"9127_CR64","doi-asserted-by":"crossref","unstructured":"Klein, C., Roidot, K.: Fourth order time-stepping for small dispersion Kadomtsev\u2013Petviashvili and Davey\u2013Stewartson equations. SIAM J. Sci. Comput. 33(6). doi: 10.1137\/100816663 (2011)","DOI":"10.1137\/100816663"},{"key":"9127_CR65","volume-title":"Recent Progress in Scientific Computing","author":"C. Klein","year":"2007","unstructured":"Klein, C., Sparber, C.: Numerical simulation of generalized KP type equations with small dispersion. In: Liu, W.-B., Ng, M., Shi, Z.-C. (eds.) Recent Progress in Scientific Computing. Science Press, Beijing (2007)"},{"key":"9127_CR66","unstructured":"Klein, C., Sparber, C.: Transverse stability of periodic traveling waves in Kadomtsev\u2013Petviashvili equations: a numerical study (2011). Preprint, arXiv:1108.3363"},{"issue":"5","key":"9127_CR67","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/s00332-007-9001-y","volume":"17","author":"C. Klein","year":"2007","unstructured":"Klein, C., Sparber, C., Markowich, P.: Numerical study of oscillatory regimes in the Kadomtsev\u2013Petviashvili equation. J. Nonlinear Sci. 17(5), 429\u2013470 (2007)","journal-title":"J. Nonlinear Sci."},{"issue":"1","key":"9127_CR68","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00209-007-0156-x","volume":"258","author":"H. Koch","year":"2008","unstructured":"Koch, H., Tzvetkov, N.: On finite energy solutions of the KP I equation. Math. Z. 258(1), 55\u201368 (2008)","journal-title":"Math. Z."},{"issue":"2","key":"9127_CR69","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.jde.2007.08.010","volume":"242","author":"B. Kojok","year":"2007","unstructured":"Kojok, B.: Sharp well-posedness for the Kadomtsev\u2013Petviashvili\u2013Burgers (KP-B-II) equation in \u211d2. J.\u00a0Differ. Equ. 242(2), 211\u2013247 (2007)","journal-title":"J.\u00a0Differ. Equ."},{"key":"9127_CR70","unstructured":"Lannes, D.: Consistency of the KP approximation. Discrete Contin. Dyn. Syst. Suppl. 517\u2013525 (2003)"},{"key":"9127_CR71","doi-asserted-by":"crossref","first-page":"2853","DOI":"10.1088\/0951-7715\/19\/12\/007","volume":"19","author":"D. Lannes","year":"2006","unstructured":"Lannes, D., Saut, J.-C.: Weakly transverse Boussinesq systems and the KP approximation. Nonlinearity 19, 2853\u20132875 (2006)","journal-title":"Nonlinearity"},{"issue":"1","key":"9127_CR72","first-page":"353","volume":"49","author":"J.L. Levandovsky","year":"2000","unstructured":"Levandovsky, J.L.: Gain of regularity for the KP II equation. Indiana Univ. Math. J. 49(1), 353\u2013403 (2000)","journal-title":"Indiana Univ. Math. J."},{"key":"9127_CR73","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1016\/j.jde.2008.01.016","volume":"245","author":"J.L. Levandovsky","year":"2008","unstructured":"Levandovsky, J.L., Sep\u00falveda, M., Vera\u00a0Villagr\u00e1n, O.: Gain of regularity for the KP I equation. J. Differ. Equ. 245, 762\u2013808 (2008)","journal-title":"J. Differ. Equ."},{"key":"9127_CR74","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.matpur.2008.06.005","volume":"90","author":"J. Li","year":"2008","unstructured":"Li, J., Xiao, J.: Well-posedness of the fifth order KP-I equation in anisotropic spaces with nonnegative indices. J. Math. Pures Appl. 90, 338\u2013352 (2008)","journal-title":"J. Math. Pures Appl."},{"key":"9127_CR75","first-page":"191","volume":"353","author":"Y. Liu","year":"2001","unstructured":"Liu, Y.: Blow-up and instability of solitary-wave solutions to a generalized Kadomtsev\u2013Petviashvili equation. Tamsui Oxf. J. Manag. Sci. 353, 191\u2013208 (2001)","journal-title":"Tamsui Oxf. J. Manag. Sci."},{"key":"9127_CR76","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1006\/jdeq.2001.4054","volume":"180","author":"Y. Liu","year":"2002","unstructured":"Liu, Y.: Strong instability of solitary-wave solutions to a Kadomtsev\u2013Petviashvili in three dimensions. J.\u00a0Differ. Equ. 180, 153\u2013170 (2002)","journal-title":"J.\u00a0Differ. Equ."},{"issue":"2","key":"9127_CR77","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF02506406","volume":"183","author":"Y. Liu","year":"1997","unstructured":"Liu, Y., Wang, X.P.: Nonlinear stability of solitary waves of generalized Kadomtsev\u2013Petviashvili equations. Commun. Math. Phys. 183(2), 253\u2013266 (1997)","journal-title":"Commun. Math. Phys."},{"issue":"3","key":"9127_CR78","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1051\/m2an:2007033","volume":"41","author":"Y. Mammeri","year":"2007","unstructured":"Mammeri, Y.: Comparaison entre mod\u00e8les d\u2019ondes de\u00a0surface en dimension 2. Mod\u00e9l. Math. Anal. Num\u00e9r. 41(3), 513\u2013542 (2007)","journal-title":"Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"9127_CR79","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0375-9601(77)90875-1","volume":"63","author":"S.V. Manakov","year":"1977","unstructured":"Manakov, S.V., Zakharov, V.E., Bordag, L.A., Matveev, V.B.: Two-dimensional solitons of the Kadomtsev\u2013Petviashvili equation and their interaction. Phys. Lett. A 63, 205\u2013206 (1977)","journal-title":"Phys. Lett. A"},{"key":"9127_CR80","unstructured":"Mantzavinos, Fokas: The Kadomtsev\u2013Petviashvili II. Equation on the half-plane. arXiv:1006.0458v2 [math.AP]. 5 Oct 2010"},{"key":"9127_CR81","doi-asserted-by":"crossref","unstructured":"Mantzavinos, Fokas: The Kadomtsev\u2013Petviashvili I. Equation on the half-plane. arXiv:1107.5612v1 [math.AP]. 28 Jul 2011","DOI":"10.1016\/j.physd.2010.11.005"},{"issue":"7","key":"9127_CR82","first-page":"813","volume":"18","author":"B. Merlet","year":"2005","unstructured":"Merlet, B., Paumond, L.: A initial boundary-value problem for the KP II equation on a strip and on the half plane. Differ. Integral Equ. 18(7), 813\u2013839 (2005)","journal-title":"Differ. Integral Equ."},{"key":"9127_CR83","unstructured":"Minchev, B., Wright, W.: A review of exponential integrators for first order semi-linear problems. Technical Report 2, The Norwegian University of Science and Technology (2005)"},{"issue":"3","key":"9127_CR84","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1007\/s00208-011-0654-3","volume":"352","author":"T. Mizomachi","year":"2012","unstructured":"Mizomachi, T., Tzvetkov, N.: Stability of the line soliton of the KP II equation under periodic transverse perturbations. Math. Ann. 352(3), 659\u2013690 (2012)","journal-title":"Math. Ann."},{"key":"9127_CR85","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1006\/jdeq.1998.3522","volume":"152","author":"L. Molinet","year":"1999","unstructured":"Molinet, L.: On the asymptotic behavior of solutions to the (generalized) Kadomtsev\u2013Petviashvili\u2013Burgers equation. J. Differ. Equ. 152, 30\u201374 (1999)","journal-title":"J. Differ. Equ."},{"issue":"6","key":"9127_CR86","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1137\/S0036141000374634","volume":"33","author":"L. Molinet","year":"2002","unstructured":"Molinet, L., Ribaud, F.: The global Cauchy problem in Bourgain type spaces for a dispersive-dissipative semilinear equation. SIAM J. Math. Anal. 33(6), 1269\u20131296 (2002)","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"9127_CR87","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1215\/S0012-7094-02-11525-7","volume":"115","author":"L. Molinet","year":"2002","unstructured":"Molinet, L., Saut, J.C., Tzvetkov, N.: Well-posedness and ill-posedness results for the Kadomtsev\u2013Petviashvili-I equation. Duke Math. J. 115(2), 353\u2013384 (2002a)","journal-title":"Duke Math. J."},{"key":"9127_CR88","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00208-002-0338-0","volume":"324","author":"L. Molinet","year":"2002","unstructured":"Molinet, L., Saut, J.C., Tzvetkov, N.: Global well-posedness for the KP-I equation. Math. Ann. 324, 255\u2013275 (2002b). Correction: Math. Ann. 328, 707\u2013710 (2004)","journal-title":"Math. Ann."},{"issue":"2","key":"9127_CR89","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1137\/060654256","volume":"39","author":"L. Molinet","year":"2007","unstructured":"Molinet, L., Saut, J.C., Tzvetkov, N.: Remarks on the mass constraint for KP type equations. SIAM J. Math. Anal. 39(2), 627\u2013641 (2007a)","journal-title":"SIAM J. Math. Anal."},{"key":"9127_CR90","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s00220-007-0243-1","volume":"272","author":"L. Molinet","year":"2007","unstructured":"Molinet, L., Saut, J.C., Tzvetkov, N.: Global well-posedness for the KP-I equation on the background of a non localized solution. Commun. Math. Phys. 272, 775\u2013810 (2007b)","journal-title":"Commun. Math. Phys."},{"issue":"5","key":"9127_CR91","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1016\/j.anihpc.2011.04.004","volume":"28","author":"L. Molinet","year":"2011","unstructured":"Molinet, L., Saut, J.C., Tzvetkov, N.: Global well-posedness for the KP-II equation on the background of a non localized solution. Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire. 28(5), 653\u2013676 (2011)","journal-title":"Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire."},{"key":"9127_CR92","series-title":"Springer Monographs in Contemporary Mathematics","volume-title":"Theory of Solitons: The Inverse Scattering Method","author":"S. Novikov","year":"1984","unstructured":"Novikov, S., Manakov, S.V., Pitaevskii, L.P., Zakharov, V.E.: Theory of Solitons: The Inverse Scattering Method. Springer Monographs in Contemporary Mathematics. Springer, Berlin (1984)"},{"key":"9127_CR93","first-page":"1","volume":"59","author":"M. Panthee","year":"2005","unstructured":"Panthee, M.: Unique continuation property for the Kadomtsev\u2013Petviashvili (KP-II) equation. Electron. J. Differ. Equ. 59, 1\u201312 (2005)","journal-title":"Electron. J. Differ. Equ."},{"issue":"9","key":"9127_CR94","first-page":"1039","volume":"16","author":"L. Paumond","year":"2003","unstructured":"Paumond, L.: A rigorous link between KP and a Benney\u2013Luke equation. Differ. Integral Equ. 16(9), 1039\u20131064 (2003)","journal-title":"Differ. Integral Equ."},{"key":"9127_CR95","first-page":"24","volume":"57","author":"D. Pelinovsky","year":"1993","unstructured":"Pelinovsky, D., Stepanynants, Y.A.: New multisolitons of the Kadomtsev\u2013Petviashvili equations. JETP Lett. 57, 24\u201328 (1993)","journal-title":"JETP Lett."},{"key":"9127_CR96","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1002\/sapm1980633185","volume":"63","author":"L. Redekopp","year":"1980","unstructured":"Redekopp, L.: Similarity solutions of some two-dimensional nonlocal wave evolution equations. Stud. Appl. Math. 63, 185\u2013207 (1980)","journal-title":"Stud. Appl. Math."},{"key":"9127_CR97","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.anihpc.2007.09.006","volume":"26","author":"F. Rousset","year":"2009","unstructured":"Rousset, F., Tzvetkov, N.: Transverse nonlinear instability for two-dimensional dispersive models. Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire 26, 477\u2013496 (2009)","journal-title":"Ann. Inst. Henri Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"key":"9127_CR98","doi-asserted-by":"crossref","first-page":"157","DOI":"10.4310\/MRL.2010.v17.n1.a12","volume":"17","author":"F. Rousset","year":"2010","unstructured":"Rousset, F., Tzvetkov, N.: A simple criterion of transverse linear instability for solitary waves. Math. Res. Lett. 17, 157\u2013169 (2010)","journal-title":"Math. Res. Lett."},{"key":"9127_CR99","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1143\/JPSJ.40.286","volume":"40","author":"J. Satsuma","year":"1976","unstructured":"Satsuma, J.: N-soliton of the two-dimensional Korteweg\u2013de Vries equation. J. Phys. Soc. Jpn. 40, 286\u2013290 (1976)","journal-title":"J. Phys. Soc. Jpn."},{"key":"9127_CR100","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1512\/iumj.1993.42.42047","volume":"42","author":"J.-C. Saut","year":"1993","unstructured":"Saut, J.-C.: Remarks on the generalized Kadomtsev\u2013Petviashvili equations. Indiana Univ. Math. J. 42, 1011\u20131026 (1993)","journal-title":"Indiana Univ. Math. J."},{"key":"9127_CR101","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/BF00994650","volume":"39","author":"J.-C. Saut","year":"1995","unstructured":"Saut, J.-C.: Recent results on the generalized Kadomtsev\u2013Petviashvili equations. Acta Appl. Math. 39, 477\u2013487 (1995)","journal-title":"Acta Appl. Math."},{"issue":"1","key":"9127_CR102","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1006\/jdeq.1998.3534","volume":"153","author":"J.-C. Saut","year":"1999","unstructured":"Saut, J.-C., Tzvetkov, N.: The Cauchy problem for higher order KP equations. J. Differ. Equ. 153(1), 196\u2013222 (1999)","journal-title":"J. Differ. Equ."},{"issue":"4","key":"9127_CR103","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/S0021-7824(00)00156-2","volume":"79","author":"J.-C. Saut","year":"2000","unstructured":"Saut, J.-C., Tzvetkov, N.: The Cauchy problem for the fifth order KP equation. J. Math. Pures Appl. 79(4), 307\u2013338 (2000)","journal-title":"J. Math. Pures Appl."},{"key":"9127_CR104","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/PL00005577","volume":"221","author":"J.-C. Saut","year":"2001","unstructured":"Saut, J.-C., Tzvetkov, N.: On the periodic KP-I type equations. Commun. Math. Phys. 221, 451\u2013476 (2001)","journal-title":"Commun. Math. Phys."},{"key":"9127_CR105","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/S1687120004010718","volume":"1","author":"J.-C. Saut","year":"2004","unstructured":"Saut, J.-C., Tzvetkov, N.: Global well-posedness for the KP-BBM equations. Appl. Math. Res. Express 1, 1\u201316 (2004)","journal-title":"Appl. Math. Res. Express"},{"key":"9127_CR106","doi-asserted-by":"crossref","first-page":"2855","DOI":"10.1103\/PhysRevLett.77.2855","volume":"77","author":"A. Senatorski","year":"1996","unstructured":"Senatorski, A., Infeld, E.: Simulations of two-dimensional Kadomtsev\u2013Petviashvili soliton dynamics in three-dimensional space. Phys. Rev. Lett. 77, 2855\u20132858 (1996)","journal-title":"Phys. Rev. Lett."},{"key":"9127_CR107","series-title":"Applied Mathematical Sciences","volume-title":"The Nonlinear Schr\u00f6dinger Equation","author":"C. Sulem","year":"1999","unstructured":"Sulem, C., Sulem, P.-L.: The Nonlinear Schr\u00f6dinger Equation. Applied Mathematical Sciences, vol.\u00a0139. Springer, Berlin (1999)"},{"key":"9127_CR108","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1009806923447","volume":"2","author":"L.-Y. Sung","year":"1999","unstructured":"Sung, L.-Y.: Square integrability and uniqueness of the solutions of the Kadomtsev\u2013Petviashvili\u2014I equation. Math. Phys. Anal. Geom. 2, 1\u201324 (1999)","journal-title":"Math. Phys. Anal. Geom."},{"key":"9127_CR109","doi-asserted-by":"crossref","first-page":"3029","DOI":"10.1143\/JPSJ.58.3029","volume":"58","author":"M. Tajeri","year":"1989","unstructured":"Tajeri, M., Murakami, Y.: Two-dimensional periodic solutions of the Kadomtsev\u2013Petviashvili equation with positive dispersion. J. Phys. Soc. Jpn. 58, 3029\u20133032 (1989)","journal-title":"J. Phys. Soc. Jpn."},{"key":"9127_CR110","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0375-9601(90)90742-7","volume":"143","author":"M. Tajeri","year":"1990","unstructured":"Tajeri, M., Murakami, Y.: The periodic soliton resonance: solutions of the Kadomtsev\u2013Petviashvili equation with positive dispersion. Phys. Lett. A 143, 217\u2013220 (1990)","journal-title":"Phys. Lett. A"},{"key":"9127_CR111","doi-asserted-by":"crossref","first-page":"483","DOI":"10.3934\/dcds.2000.6.483","volume":"6","author":"H. Takaoka","year":"2000","unstructured":"Takaoka, H.: Global well-posedness for the Kadomtsev\u2013Petviashvili II equation. Discrete Contin. Dyn. Syst. 6, 483\u2013499 (2000)","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"9127_CR112","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1155\/S1073792801000058","volume":"8","author":"H. Takaoka","year":"2001","unstructured":"Takaoka, H., Tzvetkov, N.: On the local regularity of Kadomtsev\u2013Petviashvili\u2014II equation. Int. Math. Res. Not. 8, 77\u2013114 (2001)","journal-title":"Int. Math. Res. Not."},{"key":"9127_CR113","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1090\/conm\/200\/02515","volume":"200","author":"M.M. Tom","year":"1996","unstructured":"Tom, M.M.: On a generalized Kadomtsev\u2013Petviashvili equation. Contemp. Math.- Am. Math. Soc. 200, 193\u2013210 (1996)","journal-title":"Contemp. Math.- Am. Math. Soc."},{"key":"9127_CR114","first-page":"146","volume":"62","author":"S. Turitsyn","year":"1985","unstructured":"Turitsyn, S., Falkovitch, G.: Stability of magneto-elastic solitons and self-focusing of sound in antiferromagnets. Sov. Phys. JETP 62, 146\u2013152 (1985)","journal-title":"Sov. Phys. JETP"},{"issue":"7\u20138","key":"9127_CR115","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1080\/03605309908821468","volume":"24","author":"N. Tzvetkov","year":"1999","unstructured":"Tzvetkov, N.: On the Cauchy problem for Kadomtsev\u2013Petviashvili equation. Commun. Partial Differ. Equ. 24(7\u20138), 1367\u20131397 (1999)","journal-title":"Commun. Partial Differ. Equ."},{"key":"9127_CR116","first-page":"1289","volume":"13","author":"N. Tzvetkov","year":"2000","unstructured":"Tzvetkov, N.: Global low regularity solutions for Kadomtsev\u2013Petviashvili equation. Differ. Integral Equ. 13, 1289\u20131320 (2000)","journal-title":"Differ. Integral Equ."},{"key":"9127_CR117","doi-asserted-by":"crossref","first-page":"2485","DOI":"10.1155\/S1073792804133655","volume":"46","author":"N. Tzvetkov","year":"2004","unstructured":"Tzvetkov, N.: Long time bounds for the periodic KP II equation. Int. Math. Res. Not. 46, 2485\u20132496 (2004)","journal-title":"Int. Math. Res. Not."},{"key":"9127_CR118","first-page":"193","volume":"36","author":"S. Uka\u00ef","year":"1989","unstructured":"Uka\u00ef, S.: Local solutions of the Kadomtsev\u2013Petviashvili equation. J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math. 36, 193\u2013209 (1989)","journal-title":"J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math."},{"key":"9127_CR119","doi-asserted-by":"crossref","first-page":"261","DOI":"10.12775\/TMNA.1996.012","volume":"7","author":"Z.-Q. Wang","year":"1996","unstructured":"Wang, Z.-Q., Willem, M.: A multiplicity result for the generalized Kadomstev\u2013Petviashvili equation. Topol. Methods Nonlinear Anal. 7, 261\u2013270 (1996)","journal-title":"Topol. Methods Nonlinear Anal."},{"issue":"2","key":"9127_CR120","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/S0096-3003(00)00065-5","volume":"123","author":"A. Wazwaz","year":"2001","unstructured":"Wazwaz, A.: A computational approach to soliton solutions of the Kadomtsev\u2013Petviashvili equation. Appl. Math. Comput. 123(2), 205\u2013217 (2001)","journal-title":"Appl. Math. Comput."},{"key":"9127_CR121","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/BF01210703","volume":"108","author":"M.V. Wickerhauser","year":"1987","unstructured":"Wickerhauser, M.V.: Inverse scattering for the heat equation and evolutions in (2+1) variables. Commun. Math. Phys. 108, 67\u201389 (1987)","journal-title":"Commun. Math. Phys."},{"key":"9127_CR122","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4146-1","volume-title":"Minimax Theorems","author":"M. Willem","year":"1996","unstructured":"Willem, M.: Minimax Theorems. Birkh\u00e4user, Boston (1996)"},{"issue":"9","key":"9127_CR123","first-page":"720","volume":"28","author":"A.A. Zaitsev","year":"1983","unstructured":"Zaitsev, A.A.: Formation of stationary waves by superposition of solitons. Sov. Phys. Dokl. 28(9), 720\u2013722 (1983)","journal-title":"Sov. Phys. Dokl."},{"key":"9127_CR124","first-page":"172","volume":"22","author":"V.E. Zakharov","year":"1975","unstructured":"Zakharov, V.E.: Instability and nonlinear oscillations of solitons. JETP Lett. 22, 172\u2013173 (1975)","journal-title":"JETP Lett."},{"issue":"2","key":"9127_CR125","first-page":"167","volume":"182","author":"V.E. Zakharov","year":"1998","unstructured":"Zakharov, V.E.: Weakly nonlinear waves on the surface of an ideal finite depth fluid. Am. Math. Soc. Transl. 182(2), 167\u2013197 (1998)","journal-title":"Am. Math. Soc. Transl."},{"key":"9127_CR126","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/0167-2789(80)90011-1","volume":"1","author":"V. Zakharov","year":"1980","unstructured":"Zakharov, V., Schulman, E.: Degenerative dispersion laws, motion invariants and kinetic equations. Physica D 1, 192\u2013202 (1980)","journal-title":"Physica D"},{"key":"9127_CR127","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/BF02096873","volume":"128","author":"X. Zhou","year":"1990","unstructured":"Zhou, X.: Inverse scattering transform for the time dependent Schr\u00f6dinger equation with applications to the KP-I equation. Commun. Math. Phys. 128, 551\u2013564 (1990)","journal-title":"Commun. Math. Phys."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9127-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-012-9127-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9127-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,22]],"date-time":"2023-06-22T11:18:47Z","timestamp":1687432727000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-012-9127-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,2]]},"references-count":127,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["9127"],"URL":"https:\/\/doi.org\/10.1007\/s00332-012-9127-4","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5,2]]}}}