Integrable semi-discretization of the coupled modified KdV equations

Abstract

The discrete version of the inverse scattering method proposed by Ablowitz and Ladik is extended to solve multi-component systems. The extension enables one to solve the initial value problem, which proves directly the complete integrability of a semi-discrete version of the coupled modified Korteweg–de Vries (KdV) equations and their hierarchy. It also provides a procedure to obtain conservation laws and multi-soliton solutions of the hierarchy.