Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann–Hilbert approach

Abstract

The coupled modified nonlinear Schrödinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann–Hilbert problem for the coupled modified nonlinear Schrödinger equations is formulated. And then, through solving the obtained Riemann–Hilbert problem under the conditions of irregularity and reflectionless case, N -soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.