Publication Date

2016

Journal or Book Title

Symmetry

Abstract

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.

DOI

https://doi.org/10.3390/sym8060039

Volume

8

Special Issue

Parity-Time Symmetry in Optics and Photonics

Issue

6

License

UMass Amherst Open Access Policy

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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