Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
G. L. AlfimovF. V. Lukin's Institute of Physical Problems, Zelenograd, Moscow 103460, Russia. [email protected]P. G. KevrekidisDepartment of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515V. V. KonotopDepartmento de Física and Centro de Física da Matéria Condensada, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Prof. Gama Pinto 2, Lisboa 1649-003, PortugalMario SalernoDipartimento di Fisica “E.R. Caianiello,” Università di Salerno, I-84081 Baronissi, Salerno, ItalyIstituto Nazionale di Fisica della Materia (INFM), Unità di Salerno, Italy
2002en
ABI
Аннотация
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.
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