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The paper is devoted to nonlinear localized modes ("gap solitons") for thespatially one-dimensional Gross-Pitaevskii equation (1D GPE) with a periodicpotential and repulsive interparticle interactions. It has been recently shown(G. L. Alfimov, A. I. Avramenko, Physica D, 254, 29 (2013)) that under certainconditions all the stationary modes for the 1D GPE can be coded by bi-infinitesequences of symbols of some finite alphabet (called "codes" of the solutions).We present and justify a numerical method which allows to reconstruct theprofile of a localized mode by its code. As an example, the method is appliedto compute the profiles of gap solitons for 1D GPE with a cosine potential.

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