Abstract
The (3+1)-dimensional generalized nonlinear Schrodinger equation with variable coefficients (3D-VcgNLSE) and optical lattice is investigated. Bright and dark soliton solutions are presented by two direct ansätz. Two similar solutions are obtained in terms of the elliptic and the second type of Painlevé transcendent functions. Furthermore, hyperbolic and trigonometric solutions are studied via the G′/G-expansion method. The dynamical behaviors are demonstrated in some 3D- and contour plots.
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