Riemann-Hilbert problems and soliton solutions for a multi-component cubic-quintic nonlinear Schrodinger equation

In this paper, based on the zero curvature equation, an arbitrary order matrix spectral problem is studied and its associated multi-component cubic-quintic nonlinear Schrodinger integrable hierarchy is derived. In order to solve the multi-component cubic-quintic nonlinear Schrodinger system, a class of Riemann-Hilbert problem is proposed with appropriate transformation. Through the special Riemann-Hilbert problem, where the jump matrix is considered to be an identity matrix, the soliton solutions of all integrable equations are explicitly calculated. The specific examples of one-soliton, two-soliton and N-soliton solutions are explicitly presented. (C) 2019 Elsevier B.V. All rights reserved.