Integrable discretizations and numerical simulation for a modified coupled integrable dispersionless equation

Abstract

In this paper, we propose an integrable semi-discrete and full-discrete analogues of the modified coupled integrable dispersionless (mCID) equation that was derived recently as a two-component generalization of CID equation. The key of the integrable discretization is to find the relation between the mCID equation and the sine-Gordon equation. We complete the integrable discrete analogues based on the discrete sine-Gordon equation. Numerical simulation of one-soliton, two-soliton and breather solution are conducted based on the integrable semi-discrete scheme. We also present the Casorati determinant solution in parametric form of N-soliton solutions for the semi-discrete analogue of the mCID equation. We show that the continuum limit of the full-discrete mCID equation leads to the semi-discrete mCID equation.