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.

Keywords

• M-components nonlinear Schrödinger equations
• Riemann–Hilbert
• N-soliton solutions
• Integrable hierarchies
• Block matrix spectral problem