“School of Physics”
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| Paper IPM / P / 7248 |
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We perform the complete group classification in the class of cubic Schrödinger equations of the form iψt+ψxx+ψ2ψ*+V(t,x)ψ = 0 where V is an arbitrary complex-valued potential depending on t and x. We construct all possible inequivalent potentials for which these equations have non-trivial Lie symmetries using algebraic and compatibility methods simultaneously. Our classification essentially amends earlier works on the subject.
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