Journal
PHYSICAL REVIEW E
Volume 80, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.036607
Keywords
nonlinear equations; Schrodinger equation
Categories
Funding
- FCT [SFRH/BPD/41367/2007, NSFC60821002/F02]
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It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schroumldinger (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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