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Paper IPM / Physic / 7249  


Abstract:  
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 complexvalued 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.
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