周期势排斥型Gross-Pitaevskii方程的间隙孤子：编码和计算方法
Gap solitons for the repulsive Gross-Pitaevskii equation with periodic potential: coding and method for computation
摘要：
研究了具有周期势和粒子间相互排斥作用的一维Gross-Pitaevskii方程的非线性局域模（“间隙孤子”）.它最近被证明（G。L. Alfimov，A. I. Avramenko，Physica D，254，29（2013）），在某些条件下，1D GPE的所有静止模式都可以由一些有限字母表的符号的双无限序列（称为解的“代码”）编码。我们提出并证明了一种数值方法，它允许重建的本地化模式的配置文件，其代码。作为一个例子，该方法被应用于计算具有余弦势的一维GPE的间隙孤子的轮廓。
英文摘要：
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.
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