Wannier functions analysis of the  nonlinear Schroedingerequation with a periodic potential

Alfimov, G. L.; Kevrekidis, P. G.; Konotop, V. V.; Salerno, Mario

doi:10.1103/PhysRevE.66.046608

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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.

Titolo:	Wannier functions analysis of the nonlinear Schroedingerequation with a periodic potential
Autori:	ALFIMOV G. L. KEVREKIDIS P. G. KONOTOP V. V. SALERNO, Mario mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2002
Rivista:	PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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.
Handle:	http://hdl.handle.net/11386/1063891
Appare nelle tipologie:	1.1.2 Articolo su rivista con ISSN

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