Multi-symplectic integration of the Camassa-Holm equation

被引：69

作者：

Cohen, David ^{[1
]}

Owren, Brynjulf ^{[1
]}

Raynaud, Xavier ^{[1
]}

机构：

[1] NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2008年 / 227卷 / 11期

关键词：

Camassa-Holm equation; multi-symplecticity; Euler box scheme; peakon-antipeakon collisions; conservation laws;

D O I：

10.1016/j.jcp.2008.01.051

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The Camassa-Holm equation is rich in geometric structures, it is completely integrable, bi-Hamiltonian, and it represents geodesics for a certain metric in the group of diffeomorphism. Here two new multi-symplectic formulations for the Camassa-Holm equation are presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretisation of each formulation is exemplified by means of the Euler box scheme. Numerical experiments show that the schemes have good conservative properties, and one of them is designed to handle the conservative continuation of peakon-antipeakon collisions. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：5492 / 5512

页数：21

共 41 条

[1]

[Anonymous], 1997, DISCRETE CONT DYN-A, DOI 10.3934/dcds.1997.3.419

[2] Numerical simulation of Camassa-Holm peakons by adaptive upwinding [J].