Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-05-19
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
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.
Feng Bao-Feng
Maruno Ken-ichi
Ohta Yasuhiro
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