Multisymplectic method for the Camassa-Holm equation

Yu Zhang, Zi Chen Deng, Wei Peng Hu

科研成果: 期刊稿件文章同行评审

5 引用 (Scopus)

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.

源语言英语
文章编号7
页(从-至)1-12
页数12
期刊Advances in Difference Equations
2016
1
DOI
出版状态已出版 - 1 12月 2016

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