Nonlinear modes in the harmonic PT-symmetric potential

TL;DR

This paper explores nonlinear modes in a PT-symmetric harmonic potential, revealing bifurcation behaviors and stability enhancements through parameter adjustments, advancing understanding of nonlinear Schrödinger equations with complex potentials.

Contribution

It demonstrates that nonlinear modes from different linear eigenstates can belong to the same family and shows how tuning parameters improves mode stability.

Findings

Modes bifurcate from different eigenstates can belong to the same family.

Adjusting the PT-symmetric parameter enhances mode stability.

Stability of nonlinear modes can surpass that in real harmonic potentials.

Abstract

We study the families of nonlinear modes described by the nonlinear Schr\"odinger equation with the PT-symmetric harmonic potential $x^2-2i\alpha x$. The found nonlinear modes display a number of interesting features. In particular, we have observed that the modes, bifurcating from the different eigenstates of the underlying linear problem, can actually belong to the same family of nonlinear modes. We also show that by proper adjustment of the coefficient $\alpha$ it is possible to enhance stability of small-amplitude and strongly nonlinear modes comparing to the well-studied case of the real harmonic potential.