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Multi-symplectic integration of the Camassa-Holm equation
Department of Mathematical Sciences, NTNU.ORCID iD: 0000-0001-6490-1957
Department of Mathematical Sciences, NTNU.
Department of Mathematical Sciences, NTNU.
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
Abstract [en]

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.
Keyword [en]
Camassa-Holm equation, multi-symplecticity, Euler box scheme, peakon-antipeakon collisions, conservation laws
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-59175DOI: 10.1016/j.jcp.2008.01.051ISI: 000256501800006OAI: oai:DiVA.org:umu-59175DiVA: diva2:551376
Available from: 2012-09-11 Created: 2012-09-11 Last updated: 2017-12-07Bibliographically approved

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