A Riemann-Hilbert approach in the form of a block matrix for the coupled matrix integrable system

Abstract

The two expressions of N-soliton solutions for the coupled matrix integrable system are derived via the Riemann-Hilbert (RH) approach in the form of a block matrix. Firstly, the spectral structure of the matrix integrable system and a block matrix RH problem on the real axis are investigated. By solving the special matrix RH problem with reflectionless where a jump matrix is taken to be the identity matrix, the corresponding N-soliton solutions are computed in terms of both a summation formula and determinants. As applications, we present exact solutions of the 3-wave resonant interaction (3WRI) equations and the vector nonlinear Schrödinger (NLS) equations, respectively. Particularly, some novel dynamical behaviors for these solutions are further discussed by image simulation.