Soliton Solutions and Soliton Interactions for the Coupled Nonlinear Schrödinger Equation with Varying Coefficients

The Lax pair for coupled nonlinear Schrödinger equation with varying coefficients is presented. By using Darboux transformation the exact one- and two-soliton solutions were obtained. The evolution characteristics of the exact one- and two-soliton solution and the interactions of two neighboring solitons for different initial separation and different amplitudes ratio were discussed by split step Fourier method.