Multi-symplectic integration of the Camassa-Holm equation
2008 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, no 11, 5492-5512 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2008. Vol. 227, no 11, 5492-5512 p.
Camassa-Holm equation, multi-symplecticity, Euler box scheme, peakon-antipeakon collisions, conservation laws
IdentifiersURN: urn:nbn:se:umu:diva-59175DOI: 10.1016/j.jcp.2008.01.051ISI: 000256501800006OAI: oai:DiVA.org:umu-59175DiVA: diva2:551376