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arXiv · 1704.02547

Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities

Zhenya Yan·V. V. Konotop
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Abstract

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3)-space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

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Zhenya Yan, V. V. Konotop. 2017-04-09. Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities. https://doi.org/10.1103/physreve.80.036607

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