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 the Camassa-Holm equation.
Citation
Giuseppe Maria Coclite. Kenneth H. Karlsen. Nils Henrik Risebro. "An explicit finite difference scheme for the Camassa-Holm equation." Adv. Differential Equations 13 (7-8) 681 - 732, 2008. https://doi.org/10.57262/ade/1355867333
Information