{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:37:13Z","timestamp":1772285833240,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2004,5,1]],"date-time":"2004-05-01T00:00:00Z","timestamp":1083369600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2004,5,1]],"date-time":"2004-05-01T00:00:00Z","timestamp":1083369600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2004,5]]},"DOI":"10.1007\/bf02666024","type":"journal-article","created":{"date-parts":[[2007,7,16]],"date-time":"2007-07-16T22:01:53Z","timestamp":1184623313000},"page":"297-340","source":"Crossref","is-referenced-by-count":5,"title":["A plethora of three-dimensional periodic travelling gravity-capillary water waves with multipulse transverse profiles"],"prefix":"10.1007","volume":"14","author":[{"given":"M. D.","family":"Groves","sequence":"first","affiliation":[]},{"given":"B.","family":"Sandstede","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02666024_CR1","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1006\/jdeq.1999.3675","volume":"159","author":"A. Afendikov","year":"1999","unstructured":"Afendikov, A., and Mielke, A. 1999. Bifurcation of homoclinic orbits to a saddle-focus in reversible systems with SO(2)-symmetry.J. Diff. Eq.\n                           159, 370\u2013402.","journal-title":"J. Diff. Eq."},{"key":"BF02666024_CR2","first-page":"331","volume":"27","author":"M. Berti","year":"1998","unstructured":"Berti, M., and Bolle, P. 1998. Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium.Ann. Scuola Norm. Sup. Pisa Cl. Sci.\n                           27, 331\u2013377.","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci."},{"key":"BF02666024_CR3","first-page":"1339","volume-title":"In- ternational Conference on Differential Equations","author":"B. Buffoni","year":"2000","unstructured":"Buffoni, B., and Bolle, P. 2000. Multiplicity of algebraically decaying solitary waves. InIn- ternational Conference on Differential Equations (eds. Fiedler, B., Gr\u00f6ger, K., and Sprekels, J.), pages 1339\u20131344. River Edge, NJ: World Scientific."},{"key":"BF02666024_CR4","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s002050050141","volume":"146","author":"B. Buffoni","year":"1999","unstructured":"Buffoni, B., and Groves, M. D. 1999. A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory.Arch. Ratl. Mech. Anal.\n                           146, 183\u2013220.","journal-title":"Arch. Ratl. Mech. Anal."},{"key":"BF02666024_CR5","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1098\/rsta.1996.0020","volume":"354","author":"B. Buffoni","year":"1996","unstructured":"Buffoni, B., Groves, M. D., and Toland, J. F. 1996. A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers.Phil. Trans. Roy. Soc. Lond. A\n                           354, 575\u2013607.","journal-title":"Phil. Trans. Roy. Soc. Lond. A"},{"key":"BF02666024_CR6","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1002\/(SICI)1097-0312(199603)49:3<285::AID-CPA3>3.0.CO;2-9","volume":"49","author":"B. Buffoni","year":"1996","unstructured":"Buffoni, B., and S\u00e9r\u00e9, E. 1996. A global condition for quasi-random behaviour in a class of conservative systems.Commun. Pure Appl. Math.\n                           49, 285\u2013305.","journal-title":"Commun. Pure Appl. Math."},{"key":"BF02666024_CR7","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1080\/026811100418701","volume":"15","author":"A. Champneys","year":"2002","unstructured":"Champneys, A., and H\u00e4rterich, J. 2002. Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems.Dynam. Stab. Syst.\n                           15, 231\u2013252.","journal-title":"Dynam. Stab. Syst."},{"key":"BF02666024_CR8","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1142\/S0218127494001143","volume":"4","author":"A. R. Champneys","year":"1994","unstructured":"Champneys, A. R. 1994. Subsidiary homoclinic orbits to a saddle-focus for reversible sys- tems.Int. J. Bifurcation Chaos\n                           4, 1447\u20131482.","journal-title":"Int. J. Bifurcation Chaos"},{"key":"BF02666024_CR9","volume-title":"Doctoral thesis","author":"C. Cotter","year":"1986","unstructured":"Cotter, C. 1986. The 1\u22361 semisimple resonance. Doctoral thesis, University of California at Santa Cruz."},{"key":"BF02666024_CR10","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1137\/S0036141099354181","volume":"32","author":"W. Craig","year":"2000","unstructured":"Craig, W., and Nicholls, D. P. 2000. Traveling two- and three-dimensional capillary gravity water waves.SIAM J. Math. Anal.\n                           32, 323\u2013359.","journal-title":"SIAM J. Math. Anal."},{"key":"BF02666024_CR11","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1016\/0022-0396(76)90130-3","volume":"21","author":"R. L. Devaney","year":"1976","unstructured":"Devaney, R. L. 1976. Homoclinic orbits in Hamiltonian systems.J. Diff. Eq.\n                           21, 431\u2013138.","journal-title":"J. Diff. Eq."},{"key":"BF02666024_CR12","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/S0167-2789(01)00182-8","volume":"152-153","author":"M. D Groves","year":"2001","unstructured":"Groves, M. D. 2001. An existence theory for three-dimensional periodic travelling gravity- capillary water waves with bounded transverse profiles.Physica D\n                           152-153, 395\u2013415.","journal-title":"Physica D"},{"key":"BF02666024_CR13","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s00332-003-0530-8","volume":"13","author":"M. D. Groves","year":"2003","unstructured":"Groves, M. D., and Haragus, M. 2003. A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves.J. Nonlinear Sci.\n                           13, 397\u2013447.","journal-title":"J. Nonlinear Sci."},{"key":"BF02666024_CR14","doi-asserted-by":"publisher","first-page":"2189","DOI":"10.1098\/rsta.2002.1066","volume":"360","author":"M. D. Groves","year":"2002","unstructured":"Groves, M. D., Haragus, M., and Sun, S.-M. 2002. A dimension-breaking phenomenon in the theory of gravity-capillary water waves.Phil. Trans. Roy. Soc. Lond. A\n                           360, 2189\u20132243.","journal-title":"Phil. Trans. Roy. Soc. Lond. A"},{"key":"BF02666024_CR15","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1017\/S0308210500000809","volume":"131","author":"M. D. Groves","year":"2001","unstructured":"Groves, M. D., and Mielke, A. 2001. A spatial dynamics approach to three-dimensional gravity-capillary steady water waves.Proc. Roy. Soc. Edin. A\n                           131, 83\u2013136.","journal-title":"Proc. Roy. Soc. Edin. A"},{"key":"BF02666024_CR16","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s002200100423","volume":"219","author":"M. D. Groves","year":"2001","unstructured":"Groves, M. D., and Schneider, G. 2001. Modulating pulse solutions for a class of nonlinear wave equations.Commun. Math. Phys.\n                           219, 489\u2013522.","journal-title":"Commun. Math. Phys."},{"key":"BF02666024_CR17","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/S0997-7546(98)80023-X","volume":"17","author":"M. Haragus-Courcelle","year":"1998","unstructured":"Haragus-Courcelle, M., and Ilichev, A. 1998. Three-dimensional solitary waves in the pres- ence of additional surface effects.Eur. J. Mech. B. Fluids\n                           17, 739\u2013768.","journal-title":"Eur. J. Mech. B. Fluids"},{"key":"BF02666024_CR18","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/S0167-2789(00)00125-1","volume":"145","author":"M. Haragus-Courcelle","year":"2000","unstructured":"Haragus-Courcelle, M., and Pego, R. L. 2000. Spatial wave dynamics of steady oblique wave interactions.Physica D\n                           145, 207\u2013232.","journal-title":"Physica D"},{"key":"BF02666024_CR19","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/PL00001491","volume":"50","author":"M. Haragus-Courcelle","year":"1999","unstructured":"Haragus-Courcelle, M., and Schneider, G. 1999. Bifurcating fronts for the Taylor-Couette problem in infinite cylinders.Z. Angew. Math. Phys.\n                           50, 120\u2013151.","journal-title":"Z. Angew. Math. Phys."},{"key":"BF02666024_CR20","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1216\/RMJ-1980-10-4-679","volume":"10","author":"P. J. Holmes","year":"1980","unstructured":"Holmes, P. J. 1980. Periodic, nonperiodic and irregular motions in a Hamiltonian system.Rocky Mountain J. Math.\n                           10, 382\u2013404.","journal-title":"Rocky Mountain J. Math."},{"key":"BF02666024_CR21","first-page":"265","volume":"311","author":"G. Iooss","year":"1990","unstructured":"Iooss, G., and Kirchg\u00e4ssner, K. 1990. Bifurcation d\u2019ondes solitaires en pr\u00e9sence d\u2019une faible tension superficielle.C. R. Acad. Sci. Paris, S\u00e9r. 1\n                           311, 265\u2013268.","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r. 1"},{"key":"BF02666024_CR22","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1017\/S0308210500021119","volume":"122","author":"G. Iooss","year":"1992","unstructured":"Iooss, G., and Kirchg\u00e4ssner, K. 1992. Water waves for small surface tension: An approach via normal form.Proc. Roy. Soc. Edin. A\n                           122, 267\u2013299.","journal-title":"Proc. Roy. Soc. Edin. A"},{"key":"BF02666024_CR23","first-page":"141","volume":"31","author":"M. C. W. Jones","year":"1989","unstructured":"Jones, M. C. W. 1989. Small amplitude gravity-capillary waves in a channel of finite depth.Glasgow Math. J.\n                           31, 141\u2013160.","journal-title":"Glasgow Math. J."},{"key":"BF02666024_CR24","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/BF00916827","volume":"47","author":"T. Kapitula","year":"1996","unstructured":"Kapitula, T., and Maier-Paape, S. 1996. Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation.Z. Angew. Math. Phys.\n                           47, 265\u2013305.","journal-title":"Z. Angew. Math. Phys."},{"key":"BF02666024_CR25","volume-title":"Perturbation Theory for Linear Operators","author":"T. Kato","year":"1976","unstructured":"Kato, T. 1976.Perturbation Theory for Linear Operators, 2nd ed. New York: Springer-Verlag.","edition":"2nd ed."},{"key":"BF02666024_CR26","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/0022-0396(82)90058-4","volume":"45","author":"K. Kirchg\u00e4ssner","year":"1982","unstructured":"Kirchg\u00e4ssner, K. 1982. Wave solutions of reversible systems and applications.J. Diff. Eq.\n                           45, 113\u2013127.","journal-title":"J. Diff. Eq."},{"key":"BF02666024_CR27","first-page":"135","volume":"26","author":"K. Kirchg\u00e4ssner","year":"1988","unstructured":"Kirchg\u00e4ssner, K. 1988. Nonlinear resonant surface waves and homoclinic bifurcation.Adv. Appl. Math.\n                           26, 135\u2013181.","journal-title":"Adv. Appl. Math."},{"key":"BF02666024_CR28","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1017\/S0308210500031528","volume":"116","author":"X. B. Lin","year":"1990","unstructured":"Lin, X. B. 1990. Using Melnikov\u2019s method to solve Shilnikov\u2019s problems.Proc. Roy. Soc. Edin. A\n                           116, 295\u2013325.","journal-title":"Proc. Roy. Soc. Edin. A"},{"key":"BF02666024_CR29","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1002\/mma.1670100105","volume":"10","author":"A. Mielke","year":"1988","unstructured":"Mielke, A. 1988. Reduction of quasilinear elliptic equations in cylindrical domains with applications.Math. Meth. Appl. Sci.\n                           10, 51\u201366.","journal-title":"Math. Meth. Appl. Sci."},{"key":"BF02666024_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0097544","volume-title":"Hamiltonian and Lag rang ian Flows on Center Manifolds.","author":"A. Mielke","year":"1991","unstructured":"Mielke, A. 1991.Hamiltonian and Lag rang ian Flows on Center Manifolds. Berlin: Springer- Verlag."},{"key":"BF02666024_CR31","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF01048157","volume":"4","author":"A. Mielke","year":"1992","unstructured":"Mielke, A., Holmes, P. J., and O\u2019Reilly, O.1992. Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center.J. Dyn. Diff. Eq.\n                           4, 95\u2013126.","journal-title":"J. Dyn. Diff. Eq."},{"key":"BF02666024_CR32","unstructured":"Sandstede, B. 1993. Verzweigungstheorie homokliner Verdopplungen. Doctoral thesis, Uni- versit\u00e4t Stuttgart."},{"key":"BF02666024_CR33","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/S0167-2789(97)89488-2","volume":"106","author":"B. Sandstede","year":"1997","unstructured":"Sandstede, B., Jones, C. K. R. T., and Alexander, J. C. 1997. Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers.Physica D\n                           106, 167\u2013206.","journal-title":"Physica D"},{"key":"BF02666024_CR34","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1017\/S0308210500019387","volume":"129","author":"B. Sandstede","year":"1999","unstructured":"Sandstede, B., and Scheel, A. 1999. Essential instability of pulses and bifurcations to mod- ulated travelling waves.Proc. Roy. Soc. Edin. A\n                           129, 1263\u20131290.","journal-title":"Proc. Roy. Soc. Edin. A"},{"key":"BF02666024_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/030600192","volume":"3","author":"B. Sandstede","year":"2004","unstructured":"Sandstede, B., and Scheel, A. 2004. Defects in oscillatory media: Toward a classification.S1AM J. Appl. Dynam. Syst.\n                           3, 1\u201368.","journal-title":"S1AM J. Appl. Dynam. Syst."},{"key":"BF02666024_CR36","volume-title":"Water Waves: The Mathematical Theory with Applications","author":"J. J. Stoker","year":"1957","unstructured":"Stoker, J. J. 1957.Water Waves: The Mathematical Theory with Applications. New York: Interscience."},{"key":"BF02666024_CR37","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/978-3-322-96657-5_4","volume":"2","author":"A. Vanderbauwhede","year":"1989","unstructured":"Vanderbauwhede, A. 1989. Centre manifolds, normal forms and elementary bifurcations.Dynamics Reported 2, 89\u2013169.","journal-title":"Dynamics Reported"},{"key":"BF02666024_CR38","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/978-3-642-61243-5_4","volume":"1","author":"A. Vanderbauwhede","year":"1992","unstructured":"Vanderbauwhede, A., and Iooss, G. 1992. Centre manifold theory in infinite dimensions.Dynamics Reported\n                           1, 125\u2013163.","journal-title":"Dynamics Reported"},{"key":"BF02666024_CR39","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1006\/jdeq.2000.3922","volume":"173","author":"A. C. Yew","year":"2001","unstructured":"Yew, A. C. 2001. Multipulses of nonlinearly coupled Schr\u00f6dinger equations.J. Diff. Eq.\n                           173, 92\u2013137.","journal-title":"J. Diff. Eq."},{"key":"BF02666024_CR40","doi-asserted-by":"publisher","first-page":"5886","DOI":"10.1103\/PhysRevE.61.5886","volume":"61","author":"A. C. Yew","year":"2000","unstructured":"Yew, A. C., Sandstede, B., and Jones, C. K. R. T. 2000. Instability of multiple pulses in nonlinear Schr\u00f6dinger equations.Phys. Rev. E\n                           61, 5886\u20135892.","journal-title":"Phys. Rev. E"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02666024.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/BF02666024\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02666024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02666024.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T19:28:39Z","timestamp":1652642919000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/BF02666024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,5]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,5]]}},"alternative-id":["BF02666024"],"URL":"https:\/\/doi.org\/10.1007\/bf02666024","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,5]]}}}