A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions

被引：21

作者：

Chang, Xiangke ^{[1
,2
]}

Chen, Xiaomin ^{[1
,2
]}

Hu, Xingbiao ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Beijing, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2014年 / 263卷

基金：

中国国家自然科学基金;

关键词：

Nonisospectral Camassa-Holm equation; Multipeakon solutions; Determinant technique; PEAKON SOLUTIONS; STABILITY; SOLITONS;

D O I：

10.1016/j.aim.2014.06.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by the paper of Beals, Sattinger and Szmigielski (2000) [3], we propose an extension of the Camassa-Holm equation, which also admits the multipeakon solutions. The novel aspect is that our approach is mainly based on classic determinant technique. Furthermore, the proposed equation is shown to possess a nonisospectral Lax pair. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：154 / 177

页数：24

共 50 条

[21] The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation [J].

Lai, Shaoyong ;

Wu, Yonghong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (08) :2038-2063

[22] Self-adjointness of a generalized Camassa-Holm equation [J].

Ibragimov, N. H. ;

Khamitova, R. S. ;

Valenti, A. .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (06) :2579-2583

[23] Elastic collisions among peakon solutions for the Camassa-Holm equation [J].

Chertock, Alina ;

Liu, Jian-Guo ;

Pendleton, Terrance .

APPLIED NUMERICAL MATHEMATICS, 2015, 93 :30-46

[24] On Camassa-Holm Equation with Self-Consistent Sources and Its Solutions [J].

Huang Ye-Hui ;

Yao Yu-Qin ;

Zeng Yun-Bo .

COMMUNICATIONS IN THEORETICAL PHYSICS, 2010, 53 (03) :403-412

[25] Traveling Wave Solutions of a Generalized Camassa-Holm Equation: A Dynamical System Approach [J].

Zhang, Lina ;

Song, Tao .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015

[26] Optimal control of the viscous generalized Camassa-Holm equation [J].

Shen, Chunyu ;

Gao, Anna ;

Tian, Lixin .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (03) :1835-1846

[27] Backlund Transformations for the Camassa-Holm Equation [J].

Rasin, Alexander G. ;

Schiff, Jeremy .

JOURNAL OF NONLINEAR SCIENCE, 2017, 27 (01) :45-69

[28] The peakon limits of soliton solutions of the Camassa-Holm equation [J].

Parker, Allen ;

Matsuno, Yoshimasa .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2006, 75 (12)

[29] The Cauchy problem for the generalized Camassa-Holm equation in Besov space [J].

Yan, Wei ;

Li, Yongsheng ;

Zhang, Yimin .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (08) :2876-2901

[30] Multisoliton solutions of the two-component Camassa-Holm equation and its reductions [J].

Wang, Gaihua .

THEORETICAL AND MATHEMATICAL PHYSICS, 2023, 214 (03) :308-333

← 1 2 3 4 5 →