Symmetry classification of variable coefficient cubic-quintic nonlinear Schrödinger equations

A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrödinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that the symmetry group can be at most four-dimensional in the case of...

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Bibliographic Details
Published in:Journal of mathematical physics 2013-02, Vol.54 (2), p.1
Main Authors: Oezemir, C, Guengor, F
Format: Article
Language:English
Subjects:
Algebra
Classification
Coefficients
Lie groups
Mathematical analysis
Nonlinearity
Schrodinger equation
Schroedinger equation
Symmetry
Transformations
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Summary:A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrödinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that the symmetry group can be at most four-dimensional in the case of genuine cubic-quintic nonlinearity. It may be five-dimensional (isomorphic to the Galilei similitude algebra \documentclass[12pt]{minimal}\begin{document}$\operatorname{\mathfrak {gs}}(1)$\end{document} gs ( 1 ) ) when the equation is of cubic type, and six-dimensional (isomorphic to the Schrödinger algebra \documentclass[12pt]{minimal}\begin{document}$\mathfrak {sch}(1)$\end{document} sch ( 1 ) ) when it is of quintic type.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4789543