Multi-symplectic integration of the Camassa–Holm equation
Artikel i vetenskaplig tidskrift, 2008

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.

Euler box scheme


Camassa-Holm equation

Peakon-antipeakon collisions

Conservation laws


David Cohen

Norges teknisk-naturvitenskapelige universitet

Brynjulf Owren

Norges teknisk-naturvitenskapelige universitet

Xavier Raynaud

Norges teknisk-naturvitenskapelige universitet

Journal of Computational Physics

0021-9991 (ISSN) 1090-2716 (eISSN)

Vol. 227 11 5492-5512





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