A self-adaptive mesh method for the Camassa-Holm equation

Abstract

A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Integrable discretizations of the short pulse equation
• An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
• Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory

Cited by in corpus (1)

• Integrable discretizations of the short pulse equation