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| Paper IPM / P / 8406 |
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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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