Solitons in a nonlinear Schrodinger equation with PT-symmetric potentials and inhomogeneous nonlinearity: stability and excitation of nonlinear modes

TL;DR

This paper derives explicit nonlinear modes in PT-symmetric potentials, demonstrating their stability even when linear PT-symmetry is broken, and proposes an adiabatic excitation method validated by simulations.

Contribution

It provides explicit solutions for nonlinear modes in PT-symmetric potentials and introduces an algorithm for their stable excitation through adiabatic parameter changes.

Findings

Explicit nonlinear modes are stable even when linear PT-symmetry is broken.

An adiabatic excitation method effectively induces stable nonlinear modes.

Numerical simulations confirm the stability and excitation algorithm.

Abstract

We report branches of explicit expressions for nonlinear modes in parity-time (PT) symmetric potentials of several types. For the single-well and double-well potentials the found solutions are two-parametric and appear to be stable even when the PT-symmetry of respective underlying linear models is broken. Based on the examples of these solutions we describe an algorithm of excitation of a stable nonlinear mode in a model, whose linear limit is unstable. The method is based on the adiabatic change of the control parameter driving the mode along a branch bifurcating from a stable linear mode. The suggested algorithm is confirmed by extensive numerical simulations.