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Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss

Battelli, F and Diblík, J and Fečkan, M and Pickton, J and Pospíšil, M and Susanto, H (2015) 'Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss.' Nonlinear Dynamics, 81 (1-2). 353 - 371. ISSN 0924-090X

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Abstract

© Springer Science+Business Media Dordrecht 2015. A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain–loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 02 Jul 2015 19:26
Last Modified: 30 Jan 2019 16:19
URI: http://repository.essex.ac.uk/id/eprint/14219

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