Multisoliton solutions of the two-component Camassa-Holm equation and its reductions

被引：3

作者：

Wang, Gaihua ^{[1
]}

机构：

[1] Nanjing Inst Technol, Sch Math & Phys, Nanjing, Peoples R China

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2023年 / 214卷 / 03期

基金：

中国国家自然科学基金;

关键词：

two-component Camassa-Holm equation; two-component Hunter-Saxton equation; Backlund transformation; soliton; reduction; SOLITARY-WAVE SOLUTIONS; BLOW-UP PHENOMENA; BACKLUND-TRANSFORMATIONS; GLOBAL EXISTENCE; WELL-POSEDNESS; DEFORMATIONS; SCATTERING; STABILITY; BREAKING;

D O I：

10.1134/S0040577923030029

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Backlund transformation for an integrable two-component Camassa-Holm (2CH) equation is pre-sented and studied. It involves both dependent and independent variables. A nonlinear superposition formula is given for constructing multisoliton, multiloop, and multikink solutions of the 2CH equation. We also present solutions of the Camassa-Holm equation, the two-component Hunter-Saxton (2HS) equa-tion, and the Hunter-Saxton equation, which all arise from solutions of the 2CH equation. By appropriate limit procedures, a solution of the 2HS equation is successfully obtained from that of the 2CH equation, which is worked out with the method of Backlund transformations. By analyzing the solution, we obtain the soliton and loop solutions for 2HS equation.

引用

页码：308 / 333

页数：26

共 54 条

[1]

Ablowitz MJ., 1981, SOLITONS INVERSE SCA, DOI [10.1137/1.9781611970883, DOI 10.1137/1.9781611970883]

[2] On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type [J].

Aratyn, H ;

Gomes, JF ;

Zimerman, AH .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (05) :1099-1114

[3] On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation [J].

Aratyn, Henrik ;

Gomes, Jose Francisco ;

Zimerman, Abraham H. .

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2006, 2

[4] Acoustic scattering and the extended Korteweg-de Vries hierarchy [J].

Beals, R ;

Sattinger, DH ;

Szmigielski, J .

ADVANCES IN MATHEMATICS, 1998, 140 (02) :190-206

[5] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[6] A two-component generalization of the Camassa-Holm equation and its solutions [J].

Chen, M ;

Liu, SQ ;

Zhang, YJ .

LETTERS IN MATHEMATICAL PHYSICS, 2006, 75 (01) :1-15

[7] Hamiltonian structures and their reciprocal transformations for the r-KdV-CH hierarchy [J].

Chen, Ming ;

Liu, Si-Qi ;

Zhang, Youjin .

JOURNAL OF GEOMETRY AND PHYSICS, 2009, 59 (09) :1227-1243

[8]

Constantin A, 2000, COMMUN PUR APPL MATH, V53, P603

[9] Stability of the Camassa-Holm solitons [J].

Constantin, A ;

Strauss, WA .

JOURNAL OF NONLINEAR SCIENCE, 2002, 12 (04) :415-422

[10] On the scattering problem for the Camassa-Holm equation [J].

Constantin, A .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2008) :953-970

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