Nonlinear PT-symmetric models bearing exact solutions

H. Xu; P. G. Kevrekidis; Q. Zhou; D. J. Frantzeskakis; V. Achilleos; R. Carretero-Gonzalez

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arXiv · 1310.7635

Nonlinear PT-symmetric models bearing exact solutions

H. Xu·P. G. Kevrekidis·Q. Zhou·D. J. Frantzeskakis·V. Achilleos·R. Carretero-Gonzalez

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Abstract

We study the nonlinear Schr$\ddot{o}$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.

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H. Xu, P. G. Kevrekidis, Q. Zhou, D. J. Frantzeskakis, V. Achilleos, R. Carretero-Gonzalez. 2013-10-28. Nonlinear PT-symmetric models bearing exact solutions. https://arxiv.org/abs/1310.7635

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