Lie-Theoretical Generalization and Discretization of the Pinney Equation

AbstractA Lie group approach is adopted to construct generalized Pinney equations of two distinct types which admit nonlinear superposition principles. The procedure also provides a route to discretizations of these Pinney equations which preserves the property of admittance of a nonlinear superposition principle. To conclude, underlying linearizations are placed in the context of results forC-integrable nonlinear Schrödinger equations