An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
Abstract
An integrable semi-discretization of the Camassa-Holm equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of -soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.
Keywords
Cite
@article{arxiv.0805.2843,
title = {An integrable semi-discretization of the Camassa-Holm equation and its determinant solution},
author = {Yasuhiro Ohta and Ken-ichi Maruno and Bao-Feng Feng},
journal= {arXiv preprint arXiv:0805.2843},
year = {2009}
}