Similarity transformations and exact solutions of the (3+1)-dimensional nonlinear Schrödinger equation with spatiotemporally varying coefficients.

In this paper, an extended (3+1)-dimensional nonlinear Schrödinger equation is studied. By using similarity transformation, some exact solutions of this equation are obtained, which include soliton solutions and periodic function solutions, its nonlinear spatial modulation and external potential are affected by time and space. Based on the solution obtained previously, some figures are displayed. [ABSTRACT FROM AUTHOR]