We study the nonlinear Schro¨dinger equation with a PT-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized Duffing equation. This way, we can obtain exact soliton solutions existing in the presence of suitable PT-symmetric potentials, and study their stability and dynamics. We report interesting new features, including oscillatory instabilities of solitons and (nonlinear) PT-symmetry breaking transitions, for focusing and defocusing nonlinearities.
@article{arxiv.1310.7635,
title = {Nonlinear PT-symmetric models bearing exact solutions},
author = {H. Xu and P. G. Kevrekidis and Q. Zhou and D. J. Frantzeskakis and V. Achilleos and R. Carretero-Gonzalez},
journal= {arXiv preprint arXiv:1310.7635},
year = {2013}
}