Similarity transformation and exact solutions to the generalized (3+1)-Dimensional nonlinear Schrödinger equation with distributed coefficients

摘要

In this paper, a similarity transformation is presented to reduce the generalized (3+1)-dimensional (D) nonlinear Schrödinger equation (NLSE) with distributed coefficients to the related constant-coefficients (3+1)D NLSE. Some Jacobi elliptic function solutions are given by a generalized subequation method for the constant-coefficients equation. Thus some general solutions for the generalized (3+1)D NLSE are constructed by the similarity transformation and the Jacobi elliptic function solutions. Some figures are given to illustrate the main evolution properties of these general solutions by computer simulation.