Existence, Stability & Dynamics of Nonlinear Modes in a 2d Partially $\mathcal{PT}$ Symmetric Potential

TL;DR

This paper investigates the existence, stability, and dynamics of localized nonlinear modes in a 2D cubic Schrödinger equation with a partially $ ext{PT}$-symmetric potential, expanding understanding of complex potentials with relaxed symmetry conditions.

Contribution

It explores the properties of nonlinear modes in 2D systems with partially $ ext{PT}$-symmetry, revealing new stability and dynamical behaviors not previously characterized.

Findings

Localized modes can exist in partially $ ext{PT}$-symmetric potentials.

Some modes exhibit stability depending on system parameters.

Dynamical evolution shows unique behaviors due to partial symmetry.

Abstract

It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when the parity symmetry condition is relaxed so that the potential is invariant under reflection in only a single spatial direction. We examine the existence, stability and dynamical properties of localized modes within the cubic nonlinear Schr\"odinger equation in such a scenario of partially $\mathcal{PT}$-symmetric potential.