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Paper   IPM / Physic / 7248
School of Physics
  Title:   Lie Symmetries of (1+1)-Dimensional Cubic Schrodinger Equation with Potential
1.  N.O. Ivanova
2.  R.O. Popovych
3.  H. Eshraghi
  Status:   In Proceedings
  Proceeding: Proceedings of the Fifth International Conference on Symmetry in Non Linear Mathematical Physics, Proceedings of Institute of Mathematics of NAS of Ukraine, 2004, Part 1, P. 219--224
  Vol.:  50, Part 2
  Year:  2004
  Pages:   219-223
  Supported by:  IPM
We perform the complete group classification in the class of cubic Schrödinger equations of the form iψtxx2ψ*+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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