Abstract
An investigation of Bose–Einstein condensate in two-dimensional optical lattice potentials, formed by laser beams, is carried out. We are interested in the dynamics of Bose–Einstein condensate in a square optical lattice, where the periodic potential can lead to the stabilization of an otherwise unstable Bose–Einstein condensate. The behavior of Bose–Einstein condensate in optical lattices is described by the nonlinear Gross–Pitaevskii equation, which we treat numerically. By applying the Petviashvili iteration method, we demonstrate the existence of solitonic solutions in the case of counterpropagating matter waves, and analyze their stability.
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