Higher Dimensional Gaussian-Type Solitons of Nonlinear Schrödinger Equation with Cubic and Power-Law Nonlinearities in PT-Symmetric Potentials

Two families of Gaussian-type soliton solutions of the (n+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in [Image: see text]-symmetric potentials are analytically derived. As an example, we discuss some dynamical behaviors of two dimensional soliton solutions. Their phase switches, powers and transverse power-flow densities are discussed. Results imply that the powers flow and exchange from the gain toward the loss regions in the [Image: see text] cell. Moreover, the linear stability analysis and the direct numerical simulation are carried out, which indicates that spatial Gaussian-type soliton solutions are stable below some thresholds for the imaginary part of [Image: see text]-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media.