Gap solitons for the repulsive Gross-Pitaevskii equation with periodic potential: coding and method for computation
arXiv:1609.00657 · doi:10.3934/dcdsb.2017059
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.
arXiv comment24 pages, 10 figures; accepted for DCDS-B
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Cited by in corpus (3)
- Global search for localised modes in scalar and vector nonlinear Schrödinger-type equations
- Stability of gap soliton complexes in the nonlinear Schrödinger equation with periodic potential and repulsive nonlinearity
- Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach