Symmetry breaking of solitons in two-dimensional complex potentials

TL;DR

This paper investigates symmetry breaking in two-dimensional complex potentials within the nonlinear Schrödinger equation, revealing novel bifurcation behaviors and stability properties of asymmetric solitons in partially parity-time-symmetric systems.

Contribution

It demonstrates that symmetry breaking of solitons is possible in a special class of complex potentials, with detailed analysis of bifurcation and stability properties.

Findings

Symmetry breaking bifurcation occurs in specific complex potentials.

Asymmetric solitons exhibit unique stability behaviors near bifurcation.

Bifurcated solitons can have different instability characteristics despite similar properties.

Abstract

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schr\"odinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, such symmetry breaking is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel stability properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenvalues and thus exhibit non-reciprocal nonlinear evolutions under random-noise perturbations.