Stability of solitons in PT-symmetric couplers
Rodislav Driben (1, 2), and Boris A. Malomed (2) ((1) Jerusalem, College of Engineering - Ramat Beit HaKerem, Jerusalem, Israel (2) Department, of Physical Electronics, School of Electrical Engineering, Tel Aviv, University, Tel Aviv, Israel)
TL;DR
This paper analytically and numerically investigates the stability of symmetric and antisymmetric solitons in PT-symmetric dual-core systems with Kerr nonlinearity, revealing stability regions, collision behaviors, and instability management strategies.
Contribution
It provides the first analytical stability criteria for PT-symmetric solitons and explores their dynamics, including merging and instability suppression methods.
Findings
Analytical stability region for PT-symmetric solitons
Numerical stability border for antisymmetric solitons
Elastic collision behavior of moving solitons
Abstract
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").
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