2002/05/19 by G. L. Alfimov, P. G. Kevrekidis, V. V. Konotop +2 · 3 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #cond-mat
paper · pdf · doi:10.1103/physreve.66.046608
5 pages, 1 figure, submitted to Phys. Rev. E
arxiv created 2002/05/19 · openalex publication_date 2002/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.