Phys. Rev. E 80, 036607 (2009) [9 pages]Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearitiesSee Also: Publisher's Note Received 4 May 2009; published 28 September 2009; corrected 7 October 2009 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. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.80.036607
DOI:
10.1103/PhysRevE.80.036607
PACS:
05.45.Yv, 03.75.Lm, 42.65.Tg
See AlsoPublisher's Note: Zhenya Yan and V. V. Konotop, Publisher's Note: Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities [Phys. Rev. E 80, 036607 (2009)], Phys. Rev. E 80, 049903 (2009). |
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