An explicit finite difference scheme for the Camassa-Holm equation

Abstract

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.

45 pages, 6 figures

References in corpus (1)

• Wave Structures and Nonlinear Balances in a Family of 1+1 Evolutionary PDEs