An integrable semi-discrete Degasperis-Procesi equation

Abstract

Based on our previous work to the Degasperis-Procesi equation (J. Phys. A 46 045205) and the integrable semi-discrete analogue of its short wave limit (J. Phys. A 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Meanwhile, $N$-soliton solution to the semi-discrete Degasperis-Procesi equation is provided and proved. It is shown that the proposed semi-discrete Degasperis-Procesi equation, along with its $N$-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuous limit.

20 pages

References in corpus (5)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Inverse Scattering Transform for the Degasperis-Procesi Equation
• Integrable discretizations of the short pulse equation
• An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
• Integrable semi-discretization of a multi-component short pulse equation

Cited by in corpus (1)

• Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation