TY - JOUR
T1 - An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
AU - Ohta, Yasuhiro
AU - Maruno, Ken Ichi
AU - Feng, Bao Feng
PY - 2008/9/5
Y1 - 2008/9/5
N2 - An integrable semi-discretization of the Camassa-Holm (CH) 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.
AB - An integrable semi-discretization of the Camassa-Holm (CH) 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.
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U2 - 10.1088/1751-8113/41/35/355205
DO - 10.1088/1751-8113/41/35/355205
M3 - Article
AN - SCOPUS:49749095564
VL - 41
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 35
M1 - 355205
ER -