Darboux transformation and soliton-like solutions of nonlinear Schrödinger equations

In this Letter, a systematic method is presented to construct the Darboux transformation with multi-parameters for the coupled nonlinear Schrödinger equations, from which the solutions of Schrödinger equations are reduced to solving a linear algebraic system and a constraint differential equation. With the aid of symbolic computation, new soliton-like solutions for the nonlinear Schrödinger equations are obtained by using its Darboux transformation.