title: Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential.
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.
authors.affiliation: F. V. Lukin's Institute of Physical Problems, Zelenograd, Moscow 103460, Russia. alfimov@nonlin.msk.ru
authors.forename: G L
authors.initials: GL
authors.lastname: Alfimov
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: V V
authors.initials: VV
authors.lastname: Konotop
authors.forename: M
authors.initials: M
authors.lastname: Salerno