Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity

TL;DR

This paper derives and analyzes stable Gaussian-shaped localized modes in parity-time-symmetric potentials with power-law nonlinearities, demonstrating their stability through analytical solutions and numerical simulations in multiple dimensions.

Contribution

It provides explicit analytical expressions for stable Gaussian solitons supported by PT-symmetric potentials with power-law nonlinearity, extending understanding in (1+1) and (2+1) dimensions.

Findings

Localized modes are stable over a wide parameter range.

Analytical solutions match numerical simulations.

Dynamical properties like power flow are characterized.

Abstract

We address the existence and stability of spatial localized modes supported by a parity-time-symmetric complex potential in the presence of power-law nonlinearity. The analytical expressions of the localized modes, which are Gaussian in nature, are obtained in both (1+1) and (2+1) dimensions. A linear stability analysis corroborated by the direct numerical simulations reveals that these analytical localized modes can propagate stably for a wide range of the potential parameters and for various order nonlinearities. Some dynamical characteristics of these solutions, such as the power and the transverse power-flow density, are also examined.