Darboux Transformations Of A Novel Generalization Of The Nonlinear Schr(?)dinger Equation And Its Exact Solutions

The main aim of the present paper is to construct a Darboux transformation for a novel integrable generalization of the nonlinear Schrodinger equation and its exact solu-tions. There are four sections in this paper. In section 1, we describe the development of the soliton theory and current situation and the fundamental theory of the Darboux transformation. In section 2, we first introduce the Lax pair of a coupled novel integrable generalization of the nonlinear Schrodinger equation. Then a Darboux transformation for the coupled novel integrable generalization of the nonlinear Schrodinger equation is de-rived with the help of the gauge transformation between the Lax pair. In section 3, the Darboux transformation for a novel integrable generalization of the nonlinear Schrodinger equation is obtained through the reduction techniques. A systematic algebraic procedure is given in detail to solve the novel integrable generalization of the nonlinear Schrodinger equation. In the final section, we discuss an arithmetic of the N-soliton solution of the novel integrable generalization of the nonlinear Schrodinger equation. As an application, we obtain one-soliton and two-soliton by using the Darboux transformation. Moreover, with the aid of the Mathematica, the figures of one-soliton and two-solitonwe are given through the suitably chosen parameters.