A multi-symplectic numerical integrator for the two-component Camassa–Holm equation
Journal article, 2014

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.

Casimir function

Numerical discretisation

Multi-symplectic schemes

Two-component Camassa-Holm equation

Hamiltonian PDE

Euler box scheme

Multi-symplectic formulation


David Cohen

Umeå University

Takayasu Matsuo

University of Tokyo

Xavier Raynaud

Norwegian University of Science and Technology (NTNU)

Journal of Nonlinear Mathematical Physics

1402-9251 (ISSN)

Vol. 21 3 442-453

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