Group classification of (1+1)-dimensional Schrödinger equations with potentials and power nonlinearities

We perform the complete group classification in the class of nonlinear Schrödinger equations of the form iψ t +ψ xx +|ψ| γ ψ+V(t,x)ψ=0, where V is an arbitrary complex-valued potential depending on t and x, γ is a real nonzero constant. We construct all the possible inequivalent potentials for which...

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Bibliographic Details
Published in:Journal of mathematical physics 2004-08, Vol.45 (8), p.3049-3057
Main Authors: Popovych, Roman O., Ivanova, Nataliya M., Eshraghi, Homayoon
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
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Summary:We perform the complete group classification in the class of nonlinear Schrödinger equations of the form iψ t +ψ xx +|ψ| γ ψ+V(t,x)ψ=0, where V is an arbitrary complex-valued potential depending on t and x, γ is a real nonzero constant. We construct all the possible inequivalent potentials for which these equations have nontrivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1765748