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Open AccessArticle

A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling

1
Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla. Escuela Politécnica Superior, C/Virgen de África, 7, 41011-Sevilla, Spain
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Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012-Sevilla, Spain
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Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Blas Manuel Rodríguez-Lara
Symmetry 2016, 8(6), 39; https://doi.org/10.3390/sym8060039
Received: 7 April 2016 / Revised: 8 May 2016 / Accepted: 17 May 2016 / Published: 26 May 2016
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively. View Full-Text
Keywords: kinks and anti-kinks; soliton complexes; Frenkel–Kontorova model; cross-derivative coupling; three-body interactions kinks and anti-kinks; soliton complexes; Frenkel–Kontorova model; cross-derivative coupling; three-body interactions
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MDPI and ACS Style

Cuevas-Maraver, J.; Malomed, B.A.; Kevrekidis, P.G. A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling. Symmetry 2016, 8, 39.

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