Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity

TL;DR

This paper demonstrates that in a system with inhomogeneous defocusing nonlinearity and antisymmetric gain-loss, PT-symmetry remains unbroken, supporting always stable bright solitons regardless of gain-loss strength, due to the non-linear nature of the system.

Contribution

It reveals a novel unbreakable PT-symmetry in a system lacking linear index modulation, supported by non-linear effects and specific gain-loss profiles.

Findings

PT-symmetry is never broken in the system.

Stable bright solitons exist for all gain-loss values.

Soliton branches merge without symmetry breaking.

Abstract

We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a PT-symmetry in the form of a purely real spectrum of modes, we show that the PT-symmetry is never broken in the present system, and that the system always supports stable bright solitons, fundamental and multi-pole ones. Such phenomenon is connected to non-linearizability of the underlying evolution equation. The increase of the gain-losses strength results, in lieu of the PT-symmetry breaking, in merger of pairs of different soliton branches, such as fundamental and dipole, or tripole and quadrupole ones. The fundamental and dipole solitons remain stable for all values of the gain-loss coefficient.