A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system

Abstract

A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrodinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N-fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit.