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

摘要

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