Gap solitons for the repulsive Gross-Pitaevskii equation with periodic potential: coding and method for computation
Pattern Formation and Solitons
2017-02-22 v1 Quantum Gases
Mathematical Physics
math.MP
Chaotic Dynamics
Abstract
The paper is devoted to nonlinear localized modes ("gap solitons") for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with a periodic potential and repulsive interparticle interactions. It has been recently shown (G. L. Alfimov, A. I. Avramenko, Physica D, 254, 29 (2013)) that under certain conditions all the stationary modes for the 1D GPE can be coded by bi-infinite sequences of symbols of some finite alphabet (called "codes" of the solutions). We present and justify a numerical method which allows to reconstruct the profile of a localized mode by its code. As an example, the method is applied to compute the profiles of gap solitons for 1D GPE with a cosine potential.
Cite
@article{arxiv.1609.00657,
title = {Gap solitons for the repulsive Gross-Pitaevskii equation with periodic potential: coding and method for computation},
author = {Georgy L. Alfimov and Pavel P. Kizin and Dmitry A. Zezyulin},
journal= {arXiv preprint arXiv:1609.00657},
year = {2017}
}
Comments
24 pages, 10 figures; accepted for DCDS-B