Multi-Soliton Solutions of the N-Component Nonlinear Schrodinger Equations via Riemann-Hilbert Approach*

In this paper, we utilize the Riemann-Hilbert approach to discuss multi-soliton solutions of the N-component nonlinear Schrodinger equations. Firstly, by transformed Lax pair, we construct the matrix valued functions P1,2 that satisfy the analyticity and normalization and the corresponding jump matrix can be determined. Then, in the reflectionless case, we get the multi-soliton solutions ql(l = 1, ..., N) of the N-component nonlinear Schrodinger equations, which are related to spectral parameters. Particularly, the 2-soliton solutions q1, q2 and q3 of the three-component nonlinear Schrodinger equations are given and the corresponding 2-soliton diagrams are drawn.