{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T05:58:11Z","timestamp":1742968691362,"version":"3.40.3"},"publisher-location":"New York, NY","reference-count":38,"publisher":"Springer New York","isbn-type":[{"type":"print","value":"9780387758886"},{"type":"electronic","value":"9780387304403"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-0-387-30440-3_504","type":"book-chapter","created":{"date-parts":[[2009,6,17]],"date-time":"2009-06-17T16:22:15Z","timestamp":1245255735000},"page":"8453-8457","source":"Crossref","is-referenced-by-count":1,"title":["Soliton Perturbation"],"prefix":"10.1007","author":[{"given":"Ji-Huan","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"504_CR1_504","first-page":"311","volume-title":"Report on Waves. Fourteenth Meeting of the British Association for the Advancement of Science","author":"JS Russell","year":"1844","unstructured":"Russell JS (1844) Report on Waves. Fourteenth Meeting ofthe British Association for the Advancement of Science, John Murray, London, pp\u00a0311\u2013390"},{"key":"504_CR2_504","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1080\/14786449508620739","volume":"539","author":"DJ Korteweg","year":"1895","unstructured":"Korteweg DJ, De Vires G (1895) On the change of form oflong waves advancing in a\u00a0rectangular channel, and a\u00a0new type of longstationary wave. Phil Mag Ser 539:422\u2013443","journal-title":"Phil Mag Ser"},{"key":"504_CR3_504","unstructured":"Eilbeck C (2007) John Scott Russelland the solitary wave. Heriot-Watt University, Edinburgh http:\/\/www.ma.hw.ac.uk\/%7Echris\/scott_russell.html"},{"issue":"1","key":"504_CR4_504","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0960-0779(03)00278-9","volume":"19","author":"MS El Naschie","year":"2004","unstructured":"El Naschie MS (2004) A\u00a0review of E infinity theory and themass spectrum of high energy particle physics. Chaos SolitFract 19(1):209\u2013236","journal-title":"Chaos Solit Fract"},{"key":"504_CR5_504","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1103\/PhysRevLett.15.240","volume":"15","author":"NJ Zabusky","year":"1965","unstructured":"Zabusky NJ, Kruskal MD (1965) Interaction of \u2018Solitons\u2019 ina\u00a0collisionless plasma and the recurrence of initial states. Phys RevLett 15:240\u2013243","journal-title":"Phys Rev Lett"},{"key":"504_CR6_504","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1103\/PhysRevLett.19.1095","volume":"19","author":"CS Gardner","year":"1967","unstructured":"Gardner CS, Greene JM, Kruskal MD, Miura RM (1967) Methodfor solving the KdV equation. Phys Rev Lett 19:1095\u20131097","journal-title":"Phys Rev Lett"},{"key":"504_CR7_504","doi-asserted-by":"crossref","unstructured":"Bode M, Liehr AW, Schenk CP et al (2002) Interaction ofdissipative solitons: particle-like behavior of localized structuresin a\u00a0three-component reaction-diffusion system. Physica D (1\u20132):45\u201366","DOI":"10.1016\/S0167-2789(01)00360-8"},{"issue":"3","key":"504_CR8_504","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1038\/nphys152","volume":"1","author":"HB Braun","year":"2005","unstructured":"Braun HB, Kulda J, Roessli B et al (2005) Emergence ofsoliton chirality in a\u00a0quantum antiferromagnet. Nat Phys 1(3):159\u2013163","journal-title":"Nat Phys"},{"key":"504_CR9_504","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1088\/1367-2630\/9\/1\/004","volume":"9","author":"V Ahufinger","year":"2007","unstructured":"Ahufinger V, Mebrahtu A, Corbalan R et al (2007) Quantumswitches and quantum memories for matter-wave lattice solitons. New JPhys 9:4","journal-title":"New J Phys"},{"issue":"2","key":"504_CR10_504","first-page":"203","volume":"7","author":"JF Ye","year":"2006","unstructured":"YeJF, Zheng CL, Xie LS (2006) Exact solutions andlocalized excitations of general Nizhnik\u2013Novikov\u2013Veselov system in(2+1)\u2011dimensions via a\u00a0projective approach. Int J Nonlinear Sci NumSimul 7(2):203\u2013208","journal-title":"Int J Nonlinear Sci Num Simul"},{"issue":"2","key":"504_CR11_504","first-page":"99","volume":"6","author":"JR Bogning","year":"2005","unstructured":"Bogning JR, Tchakoutio-Nguetcho AS, Kofane TC (2005) Gapsolitons coexisting with bright soliton in nonlinear fiber arrays. IntJ Nonlinear Sci Num Simul 6(4):371\u2013385; Abdusalam HA (2005) On animproved complex tanh-function method. Int J Nonlinear Sci Num Simul6(2):99\u2013106","journal-title":"Int J Nonlinear Sci Num Simul"},{"issue":"2","key":"504_CR12_504","first-page":"151","volume":"6","author":"MF El-Sabbagh","year":"2005","unstructured":"El-Sabbagh MF, Ali AT (2005) New exact solutions for(3+1)\u2011dimensional Kadomtsev\u2013Petviashvili equation and generalized(2+1)\u2011dimensional Boussinesq equation. Int J Nonlinear Sci Num Simul6(2):151\u2013162","journal-title":"Int J Nonlinear Sci Num Simul"},{"issue":"4","key":"504_CR13_504","first-page":"397","volume":"5","author":"JW Shen","year":"2004","unstructured":"Shen JW, Xu W (2004) Bifurcations of smooth andnon-smooth travelling wave solutions of the Degasperis-Procesiequation. Int J Nonlinear Sci Num Simul 5(4):397\u2013402","journal-title":"Int J Nonlinear Sci Num Simul"},{"issue":"4","key":"504_CR14_504","first-page":"1375","volume":"32","author":"Z Sheng","year":"2007","unstructured":"Sheng Z (2007) Further improved F\u2011expansion method andnew exact solutions of Kadomstev\u2013Petviashvili equation. ChaosSolit. Fract 32(4):1375\u20131383","journal-title":"Fract"},{"issue":"1\u20132","key":"504_CR15_504","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.physleta.2005.10.079","volume":"351","author":"H Yu","year":"2006","unstructured":"Yu H, Yan J (2006) Direct approach ofperturbation theory for kink solitons. Phys Lett A 351(1\u20132):97\u2013100","journal-title":"Phys Lett A"},{"issue":"5\u20137","key":"504_CR16_504","doi-asserted-by":"crossref","first-page":"e2473","DOI":"10.1016\/j.na.2005.02.034","volume":"63","author":"RL Herman","year":"2005","unstructured":"Herman RL (2005) Exploring the connection betweenquasistationary and squared eigenfunction expansion techniques insoliton perturbation theory. Nonlinear Anal 63(5\u20137):e2473\u2013e2482","journal-title":"Nonlinear Anal"},{"issue":"1","key":"504_CR17_504","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.chaos.2005.10.100","volume":"29","author":"JH He","year":"2006","unstructured":"He JH, Wu XH (2006) Construction of solitary solution andcompacton-like solution by variational iteration method. ChaosSolit Fract 29(1):108\u2013113","journal-title":"Chaos Solit Fract"},{"issue":"3","key":"504_CR18_504","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/j.chaos.2005.03.006","volume":"26","author":"JH He","year":"2005","unstructured":"He JH (2005) Application of homotopy perturbation methodto nonlinear wave equations. Chaos Solit Fract 26(3):695\u2013700","journal-title":"Chaos Solit Fract"},{"issue":"4","key":"504_CR19_504","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/S0960-0779(03)00265-0","volume":"19","author":"JH He","year":"2004","unstructured":"He JH (2004) Variational principles for some nonlinearpartial differential equations with variable coefficients. ChaosSolit Fract 19(4):847\u2013851","journal-title":"Chaos Solit Fract"},{"issue":"4","key":"504_CR20_504","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/S0020-7462(98)00048-1","volume":"34","author":"JH He","year":"1999","unstructured":"He JH (1999) Variational iteration method\u00a0\u2013 a\u00a0kind ofnon-linear analytical technique: Some examples. Int J Non-LinearMech 34(4):699\u2013708","journal-title":"Int J Non-Linear Mech"},{"issue":"4","key":"504_CR21_504","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1016\/j.chaos.2005.11.050","volume":"32","author":"EM Abulwafa","year":"2007","unstructured":"Abulwafa EM, Abdou MA, Mahmoud AA (2007) Nonlinear fluidflows in pipe-like domain problem using variational-iteration method.Chaos Solit Fract 32(4):1384\u20131397","journal-title":"Chaos Solit Fract"},{"issue":"2","key":"504_CR22_504","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.physa.2006.09.033","volume":"375","author":"M Inc","year":"2007","unstructured":"Inc M (2007) Exact and numerical solitons with compactsupport for nonlinear dispersive K(m,p) equations by the variationaliteration method. Phys A 375(2):447\u2013456","journal-title":"Phys A"},{"issue":"2","key":"504_CR23_504","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.chaos.2005.08.054","volume":"29","author":"AA Soliman","year":"2006","unstructured":"Soliman AA (2006) A\u00a0numerical simulation and explicitsolutions of KdV-Burgers' and Lax's seventh-order KdVequations. Chaos Solit Fract 29(2):294\u2013302","journal-title":"Chaos Solit Fract"},{"issue":"2","key":"504_CR24_504","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.cam.2004.11.032","volume":"181","author":"MA Abdou","year":"2005","unstructured":"Abdou MA, Soliman AA (2005) Variational iteration method for solving Burger's and coupled Burger's equations. J\u00a0Comput Appl Math 181(2):245\u2013251","journal-title":"J Comput Appl Math"},{"issue":"1","key":"504_CR25_504","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0020-7462(98)00085-7","volume":"35","author":"JH He","year":"2000","unstructured":"He JH (2000) A\u00a0coupling method of a\u00a0homotopy techniqueand a\u00a0perturbation technique for non-linear problems. Int J Non-Linear Mech 35(1):37\u201343","journal-title":"Int J Non-Linear Mech"},{"issue":"2","key":"504_CR26_504","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.physleta.2006.03.039","volume":"356","author":"DD Ganji","year":"2006","unstructured":"Ganji DD, Rafei M (2006) Solitary wave solutions for a\u00a0generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. Phys Lett A 356(2):131\u2013137","journal-title":"Phys Lett A"},{"key":"504_CR27_504","first-page":"113","volume":"8","author":"DH Shou","year":"2007","unstructured":"Shou DH, He JH (2007) Application of Parameter-expandingMethod to Strongly Nonlinear Oscillators. Int J Nonlinear Sci NumerSimul 8:113\u2013116","journal-title":"Int J Nonlinear Sci Numer Simul"},{"key":"504_CR28_504","first-page":"257","volume":"2","author":"JH He","year":"2001","unstructured":"He JH (2001) Bookkeeping parameter in perturbationmethods. Int J Nonlinear Sci Numer Simul 2:257\u2013264","journal-title":"Int J Nonlinear Sci Numer Simul"},{"key":"504_CR29_504","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0020-7462(00)00116-5","volume":"37","author":"JH He","year":"2002","unstructured":"He JH (2002) Modified Lindstedt-Poincare methods forsome strongly non-linear oscillations. Part I: expansion of a\u00a0constant. Int J Non-Linear Mech 37:309\u2013314","journal-title":"Int J Non-Linear Mech"},{"issue":"1","key":"504_CR30_504","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.cam.2006.07.020","volume":"207","author":"L Xu","year":"2007","unstructured":"Xu L (2007) He's parameter-expanding methods for stronglynonlinear oscillators. J\u00a0Comput Appl Math 207(1):148\u2013157","journal-title":"J Comput Appl Math"},{"issue":"3","key":"504_CR31_504","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1016\/j.chaos.2006.03.020","volume":"30","author":"J-H He","year":"2006","unstructured":"He J-H, Wu X-H (2006) Exp-function method fornonlinear wave equations. Chaos Solit Fract 30(3):700\u2013708","journal-title":"Chaos Solit Fract"},{"issue":"5","key":"504_CR32_504","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1016\/j.chaos.2006.05.072","volume":"34","author":"J-H He","year":"2007","unstructured":"He J-H, Abdou MA (2007) New periodic solutions fornonlinear evolution equations using Exp-function method. ChaosSolit Fract 34(5):1421\u20131429","journal-title":"Chaos Solit Fract"},{"issue":"3","key":"504_CR33_504","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1016\/j.chaos.2007.01.024","volume":"38","author":"X-H Wu","year":"2008","unstructured":"Wu X-H, He J-H (2008) EXP-function method and itsapplication to nonlinear equations. Chaos Solit Fract 38(3):903\u2013910","journal-title":"Chaos Solit Fract"},{"issue":"5","key":"504_CR34_504","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.chaos.2003.11.001","volume":"20","author":"MS El Naschie","year":"2004","unstructured":"El Naschie MS (2004) Gravitational instanton in Hilbertspace and the mass of high energy elementary particles. Chaos SolitFract 20(5):917\u2013923","journal-title":"Chaos Solit Fract"},{"issue":"1","key":"504_CR35_504","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.chaos.2003.12.001","volume":"21","author":"MS El Naschie","year":"2004","unstructured":"El Naschie MS (2004) How gravitational instanton couldsolve the mass problem of the standard model of high energy particlephysics. Chaos Solit Fract 21(1):249\u2013260","journal-title":"Chaos Solit Fract"},{"key":"504_CR36_504","first-page":"1141","volume":"20(10)","author":"JH He","year":"2006","unstructured":"He JH (2006) Some Asymptotic Methods for StronglyNonlinear Equations. Int J Mod Phys B 20(10):1141\u20131199;20(18):2561\u20132568","journal-title":"Int J Mod Phys B"},{"key":"504_CR37_504","unstructured":"He JH (2006) Non-perturbative methods for stronglynonlinear problems. dissertation.de-Verlag im Internet, Berlin"},{"key":"504_CR38_504","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139172059","volume-title":"Solitons: An Introduction","author":"PG Drazin","year":"1989","unstructured":"Drazin PG, Johnson RS (1989) Solitons: AnIntroduction. Cambridge University Press, Cambridge"}],"container-title":["Encyclopedia of Complexity and Systems Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-0-387-30440-3_504","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T05:15:52Z","timestamp":1724303752000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-0-387-30440-3_504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9780387758886","9780387304403"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-0-387-30440-3_504","relation":{},"subject":[],"published":{"date-parts":[[2009]]}}}