To main content

A multi-symplectic numerical integrator for the two-component Camassa-Holm equation

Abstract

A new multi-symplectic formulation of the two-component Camassa-Holm equation (2CH) is presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. Furthermore, this scheme preserves exactly two discrete versions of the Casimir functions of 2CH. Numerical experiments show that the proposed numerical scheme has good conservation properties.

Category

Academic article

Language

English

Author(s)

  • David Cohen
  • Takayasu Matsuo
  • Xavier Raynaud

Affiliation

  • Umeå University
  • The University of Tokyo
  • Norwegian University of Science and Technology
  • SINTEF Digital / Mathematics and Cybernetics

Year

2014

Published in

Journal of Nonlinear Mathematical Physics

ISSN

1402-9251

Publisher

Springer

Volume

21

Issue

3

Page(s)

442 - 453

View this publication at Cristin