Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2016, Article ID 9514230, 12 pages
http://dx.doi.org/10.1155/2016/9514230
Research Article

Bright Solitons in a -Symmetric Chain of Dimers

1Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, UK
2Department of Mathematics, University of Indonesia, Depok, Indonesia

Received 17 July 2016; Revised 17 September 2016; Accepted 17 October 2016

Academic Editor: Yao-Zhong Zhang

Copyright © 2016 Omar B. Kirikchi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence and stability of fundamental bright discrete solitons in a parity-time- (-) symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.