Kirikchi, Omar B and Bachtiar, Alhaji A and Susanto, Hadi
(2016)
*Bright Solitons in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Chain of Dimers.*
Advances in Mathematical Physics, 2016.
pp. 1-12.
DOI https://doi.org/10.1155/2016/9514230

Kirikchi, Omar B and Bachtiar, Alhaji A and Susanto, Hadi
(2016)
*Bright Solitons in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Chain of Dimers.*
Advances in Mathematical Physics, 2016.
pp. 1-12.
DOI https://doi.org/10.1155/2016/9514230

Kirikchi, Omar B and Bachtiar, Alhaji A and Susanto, Hadi
(2016)
*Bright Solitons in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Chain of Dimers.*
Advances in Mathematical Physics, 2016.
pp. 1-12.
DOI https://doi.org/10.1155/2016/9514230

## Abstract

<jats:p>We study the existence and stability of fundamental bright discrete solitons in a parity-time- (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-) 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.</jats:p>

Item Type: | Article |
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Additional Information: | (Invited paper) Advances in Mathematical Physics (2016) |

Uncontrolled Keywords: | nlin.PS; physics.optics |

Subjects: | Q Science > QA Mathematics Q Science > QC Physics |

Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of |

SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |

Depositing User: | Unnamed user with email elements@essex.ac.uk |

Date Deposited: | 06 Dec 2016 12:16 |

Last Modified: | 23 Sep 2022 18:43 |

URI: | http://repository.essex.ac.uk/id/eprint/18363 |

## Available files

**Filename:** 9514230.pdf

**Licence: **Creative Commons: Attribution 3.0