Volume 21, Issue 3, June 2014, Pages 442 - 453
A multi-symplectic numerical integrator for the two-component Camassa–Holm equation
Authors
David Cohen
Matematik och matematisk statistik, Umeå universitet 90187 Umeå, Sweden,david.cohen@math.umu.se
Takayasu Matsuo
Department of Mathematical Informatics, Graduate School of System of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku 113-8656 Tokyo, Japan,matsuo@mist.i.u-tokyo.ac.jp
Xavier Raynaud
Applied Mathematics, SINTEF ICT Forskningsveien 1, 0373 Oslo, Norway
Department of Mathematical Science, NTNU 7491 Trondheim, Norway,xav.raynaud@gmail.com
Received 19 February 2014, Accepted 16 May 2014, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2014.936763How to use a DOI?
- Keywords
- Two-component Camassa–Holm equation; Hamiltonian PDE; Casimir function; Numerical discretisation; Multi-symplectic formulation; Multi-symplectic schemes; Euler box scheme
- 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.
- Copyright
- © 2014 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - David Cohen AU - Takayasu Matsuo AU - Xavier Raynaud PY - 2021 DA - 2021/01/06 TI - A multi-symplectic numerical integrator for the two-component Camassa–Holm equation JO - Journal of Nonlinear Mathematical Physics SP - 442 EP - 453 VL - 21 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2014.936763 DO - 10.1080/14029251.2014.936763 ID - Cohen2021 ER -