ar X iv : 0 80 2 . 31 29 v 1 [ m at h . A P ] 2 1 Fe b 20 08 AN EXPLICIT FINITE DIFFERENCE SCHEME FOR THE CAMASSA - HOLM EQUATION
نویسنده
چکیده
We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H 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 towards a dissipative weak solution of Camassa-Holm equation.
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