Multisymplectic method for the Camassa-Holm equation

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• 作者：Yu Zhang ; Zi-Chen Deng ; Wei-Peng Hu
• 关键词：35Q51 ; 37K10 ; 65P10 ; multisymplectic method ; Camassa ; Holm equation ; conservation law ; peaked wave solution
• 刊名：Advances in Difference Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,624 KB
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• 作者单位：Yu Zhang (1)
  Zi-Chen Deng (1)
  Wei-Peng Hu (1)
  
  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, Shannxi, 710072, P.R. China
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

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. Keywords multisymplectic method Camassa-Holm equation conservation law peaked wave solution