Evolution of the exact spatiotemporal periodic wave and soliton solutions of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients

Abstract

In this paper the spatiotemporal evolution of the periodic wave is investigated analytically when the laser passes through the inhomogeneous nonlinear medium. Firstly, the (3+1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients is solved analytically by an improved homogeneous balance principle and F-expansion technique. A number of exact periodic traveling wave and spatiotemporal soliton solutions are obtained. Then, their propagation characteristics are analyzed in detail. It is found that the evolutions of propagation of spatiotemporal soliton and periodic wave solutions are regular when the diffraction and dispersion coefficients are the identical distributed coefficients, but the evolutions of propagation of these solutions are irregular with other coefficients.