An integrable semi-discrete Degasperis–Procesi equation

Abstract

Based on our previous work on the Degasperis–Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis–Procesi equation by Hirota's bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis–Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis–Procesi equation, and its N-soliton solution converge to ones of the original Degasperis–Procesi equation in the continuum limit.

Locations

• Nonlinearity - View
• arXiv (Cornell University) - View - PDF