2008/05/31 by Yasuhiro Ohta, Ken-ichi Maruno, Bao-Feng Feng · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP #nlin.PS
paper · pdf · doi:10.1088/1751-8113/41/35/355205
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 N-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.