Publication Date

2002

Journal or Book Title

Physics Review E

Abstract

In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödinger equation with a periodic potential is equivalent to a vector lattice with long-range interactions. For the case-example of the cosine potential we study the validity of the so-called tight-binding approximation, i.e., the approximation when nearest neighbor interactions are dominant. The results are relevant to the Bose-Einstein condensate theory as well as to other physical systems, such as, for example, electromagnetic wave propagation in nonlinear photonic crystals.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v66/i4/e046608

Volume

66

Issue

4

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