Title: Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities,
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.