2016/09/02 by Georgy L. Alfimov, Pavel P. Kizin, Dmitry A. Zezyulin · 1 citation
Physics and Astronomy · Mathematics · #nlin.PS #cond-mat.quant-gas #math-ph #math.MP #nlin.CD #msc:35Q55 #msc:35C08 #msc:34C41 #msc:37B10 #msc:65P99
paper · pdf · doi:10.3934/dcdsb.2017059
published as Discrete and Continuous Dynamical Systems - Series B 22, 1207 - 1229 (2017) · 24 pages, 10 figures; accepted for DCDS-B
arxiv created 2016/09/02 · arxiv updated 2017/02/22
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.