Gap solitons for the repulsive Gross-Pitaevskii equation with periodic potential: coding and method for computation

Autor:	Alfimov, Georgy L., Kizin, Pavel P., Zezyulin, Dmitry A.
Rok vydání:	2016
Předmět:	Nonlinear Sciences - Pattern Formation and Solitons Condensed Matter - Quantum Gases Mathematical Physics Nonlinear Sciences - Chaotic Dynamics 35Q55 35C08 34C41 37B10 65P99
Zdroj:	Discrete and Continuous Dynamical Systems - Series B 22, 1207 - 1229 (2017)
Druh dokumentu:	Working Paper
DOI:	10.3934/dcdsb.2017059
Popis:	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. Comment: 24 pages, 10 figures; accepted for DCDS-B
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1609.00657 Zobrazit plný text záznamu View this record from Arxiv