A two-component generalization of the Camassa-Holm equation and its solutions

被引：317
作者：
Chen, M [1 ]
Liu, SQ [1 ]
Zhang, YJ [1 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2006年 / 75卷 / 01期
关键词：
Camassa-Holm equation; AKNS hierarchy; reciprocal transformation;
D O I：
10.1007/s11005-005-0041-7
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
An explicit reciprocal transformation between a two-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established. This transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH system are presented.
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页码：1 / 15
页数：15
相关论文
共 33 条
[1]  
ABENTA S, MATHPH0506042
[2]  
ABLOWITZ MJ, 1974, STUD APPL MATH, V53, P249
[3]   The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and dym type [J].
Alber, MS ;
Camassa, R ;
Fedorov, YN ;
Holm, DD ;
Marsden, JE .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 221 (01) :197-227
[4]  
ALONSO LM, 1980, J MATH PHYS, V21, P2342, DOI 10.1063/1.524690
[5]   FACTORIZATION OF ENERGY-DEPENDENT SCHRODINGER-OPERATORS - MIURA MAPS AND MODIFIED SYSTEMS [J].
ANTONOWICZ, M ;
FORDY, AP .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 124 (03) :465-486
[6]   COUPLED KDV EQUATIONS WITH MULTI-HAMILTONIAN STRUCTURES [J].
ANTONOWICZ, M ;
FORDY, AP .
PHYSICA D, 1987, 28 (03) :345-357
[7]   COUPLED DYM,HARRY EQUATIONS WITH MULTI-HAMILTONIAN STRUCTURES [J].
ANTONOWICZ, M ;
FORDY, AP .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1988, 21 (05) :L269-L275
[8]   Multipeakons and the classical moment problem [J].
Beals, R ;
Sattinger, DH ;
Szmigielski, J .
ADVANCES IN MATHEMATICS, 2000, 154 (02) :229-257
[9]   AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].
CAMASSA, R ;
HOLM, DD .
PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664
[10]  
Camassa R., 1994, Adv. Appl. Mech., V31, P1, DOI DOI 10.1016/S0065-2156(08)70254-0
1234