Exact N-soliton solutions and dynamics of two types of matrix nonlinear Schrodinger equation

The dynamical properties of the optical solitons in two types of matrix nonlinear Schrodin-ger (NLS) equation are studied by Riemann-Hilbert method. Firstly, the inverse scattering transform of the matrix NLS equation is investigated and the corresponding Riemann-Hilbert problem is established. Then, by solving the Riemann-Hilbert problem of discrete spectrum, the N-soliton solutions of the matrix NLS equations are obtained. Finally, the single-soliton solution, two-soliton solution and three-soliton solution of the matrix NLS equations are attained. It is proved that the two-soliton solution is decomposed into two single-soliton solutions when the time approaches infinity and the multiple solitons will overlap and form a bound state advancing at the same velocity when they have the same velocity.