N-soliton solutions for the coupled extended modified KdV equations via Riemann–Hilbert approach

Abstract

In this paper, we utilize the Riemann–Hilbert method to construct the N-soliton solutions for the coupled extended modified KdV equations with zero boundary condition. Firstly, we establish the relationship between the solutions of the coupled extended modified KdV equations and a Riemann–Hilbert problem. Secondly, by solving the particular Riemann–Hilbert problem with an identity jump matrix, the general N-soliton solutions of the coupled extended modified KdV equations are derived. In addition, the local structures of the N-soliton solution are graphically presented by choosing parameters suitably.