On the integrability of PT-symmetric dimers
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.
Keywords
Cite
@article{arxiv.1307.2788,
title = {On the integrability of PT-symmetric dimers},
author = {J. Pickton and H. Susanto},
journal= {arXiv preprint arXiv:1307.2788},
year = {2014}
}
Comments
To appear in Physical Review A