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Paper   IPM / Physic / 7249
School of Physics
  Title:   Group Classification of (1+1)-Dimensional Schrodinger Equations with Potentials and Power Nonlinearities
  Author(s): 
1.  N.O. Ivanova
2.  H. Eshraghi
3.  R.O. Popovych
  Status:   Published
  Journal: J. Math. Phys.
  Vol.:  45
  Year:  2004
  Pages:   3049-3057
  Supported by:  IPM
  Abstract:
We perform the complete group classification in the class of nonlinear Schrödinger equations of the form iψtxx+|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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