Nonautonomous rogue wave solutions and numerical simulations for a three-dimensional nonlinear Schrödinger equation

Abstract

We consider nonautonomous rogue wave solutions of a \((3+1)\)-dimensional (3D) nonlinear Schrodinger equation (NLSE) with time–space modulation terms, the dispersion and the nonlinear coefficients engendering temporal dependency. Similarity transformation is used to convert the nonautonomous equation into autonomous NLSE; we obtain the multi-rogue wave solutions employing the generalized Darboux transformation. Particularly, the rogue wave solutions possess several free parameters. Then, the first-order and second-order nonautonomous rogue wave solutions are considered for the 3D NLSE with variable coefficients. At last, the numerical simulations on the evolution and collision of rogue wave solutions are performed to verify the prediction of the analytical formulations. The obtained nonautonomous rogue wave solutions can be used to describe the dynamics waves in the nonlinear optical fibers and Bose–Einstein condensates, respectively.