Nonlinear localized modes in PT-symmetric Rosen-Morse potential well

TL;DR

This paper explores the existence, analytical solutions, and stability of nonlinear localized modes in PT-symmetric Rosen-Morse potentials, revealing their instability despite unbroken PT-symmetry, supported by numerical simulations.

Contribution

It provides exact analytical localized modes in 1D and 2D for the nonlinear Schrödinger equation with PT-symmetric Rosen-Morse potential, and analyzes their stability.

Findings

Localized modes exist in both 1D and 2D geometries.

All localized modes are linearly unstable.

Numerical simulations confirm the instability results.

Abstract

We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.