The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation

Abstract

A four-component nonlinear Schrödinger equation associated with a 5×5 Lax pair is investigated. A spectral problem is analysed and the Jost functions are used in order to derive a Riemann-Hilbert problem connected with the equation under consideration. $N$-soliton solutions of the equation are obtained by solving the Riemann-Hilbert problem without reflection. For $N = 1$ and $N = 2$, the local structure and dynamic behavior of some special solutions are analysed by invoking their graphic representations.