Can parity-time-symmetric potentials support continuous families of non-parity-time-symmetric solitons?

TL;DR

This paper investigates whether one-dimensional PT-symmetric potentials can support continuous families of non-PT-symmetric solitons, concluding that such families are unlikely due to symmetry constraints and perturbation effects.

Contribution

It provides a theoretical analysis showing the non-existence of continuous non-PT-symmetric soliton families in 1D PT-symmetric potentials.

Findings

Weak PT-symmetric perturbations destroy asymmetric soliton families.

Symmetry breaking of PT-symmetric solitary waves does not occur in these models.

Continuous families of non-PT-symmetric solitons are unlikely in 1D PT-symmetric potentials.

Abstract

For the one-dimensional nonlinear Schroedinger equations with parity-time (PT) symmetric potentials, it is shown that when a real symmetric potential is perturbed by weak PT-symmetric perturbations, continuous families of asymmetric solitary waves in the real potential are destroyed. It is also shown that in the same model with a general PT-symmetric potential, symmetry breaking of PT-symmetric solitary waves do not occur. Based on these findings, it is conjectured that one-dimensional PT-symmetric potentials cannot support continuous families of non-PT-symmetric solitary waves.