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
Author
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 3 442-453Subject Categories
Mathematics
DOI
10.1080/14029251.2014.936763