A self-adaptive mesh method for the Camassa-Holm equation
Exactly Solvable and Integrable Systems
2010-04-27 v3 Pattern Formation and Solitons
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.
Cite
@article{arxiv.0905.2693,
title = {A self-adaptive mesh method for the Camassa-Holm equation},
author = {Bao-Feng Feng and Ken-ichi Maruno and Yasuhiro Ohta},
journal= {arXiv preprint arXiv:0905.2693},
year = {2010}
}