Multisymplectic method for the Camassa-Holm equation

Advances in Difference Equations

Yu Zhang¹  Wei-Peng Hu¹  Zi-Chen Deng² 

[1] School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, P.R. China

关键词: multisymplectic method;    Camassa-Holm equation;    conservation law;    peaked wave solution;    35Q51;    37K10;    65P10;   

DOI  :  10.1186/s13662-015-0724-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The Camassa-Holm equation, a completely integrable evolution equation, contains rich geometric structures. For the existence of the bi-Hamiltonian structure and the so-called peaked wave solutions, considerable interest has been aroused in the last several decades. Focusing on local geometric properties of the peaked wave solutions for the Camassa-Holm equation, we propose the multisymplectic method to simulate the propagation of the peaked wave in this paper. Based on the multisymplectic theory, we present a multisymplectic formulation of the Camassa-Holm equation and the multisymplectic conservation law. Then, we apply the Euler box scheme to construct the structure-preserving scheme of the multisymplectic form. Numerical results show the merits of the multisymplectic scheme constructed, especially the local conservative properties on the wave form in the propagation process.

【 授权许可】

CC BY