An explicit finite difference scheme for the Camassa-Holm equation

Details An explicit finite difference scheme for the Camassa-Holm equation An explicit finite difference scheme for the Camassa-Holm equation

2008-02-21

arxiv.org/abs/0802.3129v1

Mathematics

Analysis of PDEs

45 pages, 6 figures

Scientific paper

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general $H^1$ initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in $H^1$ towards a dissipative weak solution of Camassa-Holm equation.

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