An integrable semi-discrete Degasperis-Procesi equation

TL;DR

This paper derives an integrable semi-discrete version of the Degasperis-Procesi equation using Hirota's bilinear method, providing explicit N-soliton solutions and demonstrating their convergence to the continuous case.

Contribution

The paper introduces a novel integrable semi-discrete Degasperis-Procesi equation and constructs its N-soliton solutions, extending previous work on related equations.

Findings

Derived an integrable semi-discrete Degasperis-Procesi equation.

Constructed explicit N-soliton solutions for the semi-discrete equation.

Proved convergence of solutions to the continuous 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.