The N-soliton solutions to the M-components nonlinear Schrödinger equations by the Riemann–Hilbert approach

Abstract

In this paper, the main work is to study the N -soliton solutions for the M -component nonlinear Schrödinger equations, the matrix Riemann–Hilbert problem is constructed for this integrable hierarchies by analyzing the block matrix spectral problem of the Lax pair, then the N -soliton solutions for this system are given explicitly by the scattering matrix. Finally, We briefly summarize the work of this article and make prospects for future work.