Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (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.
Yan
Zhenya
Z
Centro de Física Teórica e Computacional, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal. zhenyan@cii.fc.ul.pt
Konotop
V V
VV
D003198:Computer Simulation; D004574:Electromagnetic Fields; D008962:Models, Theoretical; D017711:Nonlinear Dynamics