Admissible Transformations of Nonlinear Schrödinger Equations

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 Schrödinger equations, in particular, in the class of nonlinear (1+1)-dimensional Schrödinger 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.