Stabilization of solitons in PT models with supersymmetry by periodic management

¹ Jerusalem College of Engineering, Ramat Beit HaKerem - POB 3566, Jerusalem, 91035, Israel
² Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University Tel Aviv 69978, Israel

^a radik@eng.tau.ac.il

Received: 15 August 2011
Accepted: 11 October 2011

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-core 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.