A unified and explicit construction of N-soliton solutions for the nonlinear Schrodinger equation

An explicit N-fold Darboux transformation with multiparameters for nonlinear Schrodinger equation is constructed with the help of its Lax pairs and a reduction technique. According to this Darboux transformation, the solutions of the nonlinear Schrodinger equation are reduced to solving a Linear algebraic system, from which a unified and explicit formulation of N-soliton solutions with multiparameters for the nonlinear Schrodinger equation is given.