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arXiv · 1307.2788

On the integrability of PT-symmetric dimers

J. Pickton·H. Susanto
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Abstract

The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase-portraits of the system. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behaviour of all solutions of the system, including changes in the topological structure of the phase-plane, is then discussed.

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J. Pickton, H. Susanto. 2013-12-05. On the integrability of PT-symmetric dimers. https://doi.org/10.1103/physreva.88.063840

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