A Riemann-Hilbert Approach to the Kundu-nonlinear Schrödinger equation and its multi-component generalization

Abstract In this paper, the main work is to study the N-soliton solutions for the Kundu-nonlinear Schrodinger equation. Then, the matrix Riemann-Hilbert problem is constructed for this integrable equation by analyzing the spectral problem of the Lax pair. Based on the scattering relationship, the N-soliton solutions for this system are given explicitly. Finally, the multi-component Kundu-nonlinear Schrodinger system is generalized, and reduce its N-soliton solutions.