文章基本信息

标题：Multisymplectic method for the Camassa-Holm equation
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作者：Yu Zhang ; Zi-Chen Deng ; Wei-Peng Hu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：7
DOI：10.1186/s13662-015-0724-z
语种：English
出版社：Hindawi Publishing Corporation
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.
关键词：multisymplectic method ; Camassa-Holm equation ; conservation law ; peaked wave solution