Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
Pattern Formation and Solitons
2014-06-03 v3
Abstract
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a two-element discretized version of this PT nonlinear Schr\"odinger equation. By obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself.
Cite
@article{arxiv.1310.7399,
title = {Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities},
author = {Amarendra K. Sarma and Mohammad-Ali Miri and Ziad H. Musslimani and Demetrios N. Christodoulides},
journal= {arXiv preprint arXiv:1310.7399},
year = {2014}
}