Variable coefficient nonlinear Schrödinger equations with four-dimensional symmetry groups and analysis of their solutions

Analytical solutions of variable coefficient nonlinear Schrödinger equations having four-dimensional symmetry groups, which are in fact the next closest to the integrable ones occurring only when the Lie symmetry group is five-dimensional, are obtained using two different tools. The first tool is to...

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Bibliographic Details
Published in:Journal of mathematical physics 2011-09, Vol.52 (9), p.093702-093702-19
Main Authors: Özemir, C., Güngör, F.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Lie groups
Mathematical methods in physics
Mathematics
Ordinary differential equations
Physics
Schrodinger equation
Sciences and techniques of general use
Symmetry
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Summary:Analytical solutions of variable coefficient nonlinear Schrödinger equations having four-dimensional symmetry groups, which are in fact the next closest to the integrable ones occurring only when the Lie symmetry group is five-dimensional, are obtained using two different tools. The first tool is to use one-dimensional subgroups of the full symmetry group to generate solutions from those of the reduced ordinary differential equations, namely, group invariant solutions. The other is by truncation in their Painlevé expansions.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3634005