On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity

被引：18
作者：
Munoz, Claudio [1 ]
机构：
[1] Univ Versailles St Quentin En Yvelines, LMV UMR 8100, F-78035 Versailles, France
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2010年 / 2010卷 / 09期
关键词：
KORTEWEG-DEVRIES EQUATION; ASYMPTOTIC STABILITY; SOLITARY WAVES; SOLITONS; SCATTERING; EVOLUTION; PLASMA;
D O I：
10.1093/imrn/rnp204
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the problem of two-soliton collision for the generalized Korteweg-de Vries equations, completing some recent works of Y. Martel and F. Merle [22, 25]. We classify the nonlinearities for which collisions are elastic or inelastic. Our main result states that in the case of small solitons, with one soliton smaller than the other one, the unique nonlinearities allowing a perfectly elastic collision are precisely the integrable cases, namely, the quadratic (KdV), cubic (mKdV), and Gardner nonlinearities.
引用
收藏
页码：1624 / 1719
页数：96
相关论文
共 34 条
  • [1] ABLOWITZ MJ, 1974, STUD APPL MATH, V53, P249
  • [2] Colliding Solitons for the Nonlinear Schrodinger Equation
    Abou Salem, W. K.
    Froehlich, J.
    Sigal, I. M.
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 291 (01) : 151 - 176
  • [3] [Anonymous], 1991, SOLITONS NONLINEAR E
  • [4] BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
  • [5] STABILITY AND INSTABILITY OF SOLITARY WAVES OF KORTEWEG-DEVRIES TYPE
    BONA, JL
    SOUGANIDIS, PE
    STRAUSS, WA
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1987, 411 (1841) : 395 - 412
  • [6] SOLITARY-WAVE INTERACTION
    BONA, JL
    PRITCHARD, WG
    SCOTT, LR
    [J]. PHYSICS OF FLUIDS, 1980, 23 (03) : 438 - 441
  • [7] FERMI E, 1974, NONLINEAR WAVE MOTIO, P143
  • [8] Inversion of the linearized Korteweg-deVries equation at the multi-soliton solutions
    Haragus-Courcelle, M
    Sattinger, DH
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1998, 49 (03): : 436 - 469
  • [9] EXACT SOLUTION OF KORTEWEG-DE VRIES EQUATION FOR MULTIPLE COLLISIONS OF SOLITONS
    HIROTA, R
    [J]. PHYSICAL REVIEW LETTERS, 1971, 27 (18) : 1192 - +
  • [10] Soliton splitting by external delta Potentials
    Holmer, J.
    Marzuola, J.
    Zworski, M.
    [J]. JOURNAL OF NONLINEAR SCIENCE, 2007, 17 (04) : 349 - 367
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