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| Paper IPM / P / 7249 |
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We perform the complete group classification in the class of nonlinear Schrödinger equations of the form iψt+ψxx+|ψ|γψ+V(t,x)ψ = 0 where V is an arbitrary complex-valued potential depending on t and x, γ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial 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.
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