Stabilization of solitons in PT models with supersymmetry by periodic management

TL;DR

This paper proposes a periodic management technique to stabilize solitons in PT-symmetric dual-core nonlinear waveguides with supersymmetry, transforming unstable solutions into attractors while preserving the system's symmetry.

Contribution

It introduces a novel management method involving periodic sign switching of gain, loss, and coupling to stabilize supersymmetric solitons in PT models.

Findings

Periodic management stabilizes solitons effectively.

Solitons become attractors with identifiable basins.

Amplitude asymmetry leads to quasi-stable breathers.

Abstract

We introduce a system based on dual-core nonlinear waveguides with the balanced gain and loss acting separately in the cores. The system features a "supersymmetry" when the gain and loss are equal to the inter-core coupling. This system admits a variety of exact solutions (we focus on solitons), which are subject to a specific subexponential instability. We demonstrate that the application of a "management", in the form of periodic simultaneous switch of the sign of the gain, loss, and inter-coupling, effectively stabilizes solitons, without destroying the supersymmetry. The management turns the solitons into attractors, for which an attraction basin is identified. The initial amplitude asymmetry and phase mismatch between the components transforms the solitons into quasi-stable breathers.