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Paper   IPM / Physic / 8406
School of Physics
  Title:   Admissible Transformations and Normalized Classes of Nonlinear Schroedinger Equations
  Author(s): 
1.  R. O . Popovych
2.  M. Kunzinger
3.  H. Eshraghi
  Status:   Published
  Journal: Acta Appl. Math.
  No.:  2
  Vol.:  109
  Year:  2010
  Pages:   315-359
  Supported by:  IPM
  Abstract:
The notion of a normalized class of differential equations is developed. Using it, we exhaustively describe admissible point transformations in classes of nonlinear (1+1)-dimensional Schroedinger equations, in particular, in the class of nonlinear (1+1)-dimensional Schroedinger equations with modular nonlinearities and potentials and some subclasses of this class. Then we perform complete group classification in this class, representing it as a union of disjoint normalized subclasses and applying a combination of algebraic and compatibility methods. The proposed approach can be applied to studying symmetry properties of a wide range of differential equations.


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