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Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential

G. L. Alfimov·P. G. Kevrekidis·V. V. Konotop·M. Salerno
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Abstract

In the present Letter 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 Bose-Einstein condensate theory as well as to other physical systems like, for example, electromagnetic wave propagation in nonlinear photonic crystals.

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G. L. Alfimov, P. G. Kevrekidis, V. V. Konotop, M. Salerno. 2002-05-19. Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential. https://doi.org/10.1103/physreve.66.046608

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