A nonlinear superposition rule for solutions of the Milne--Pinney equation

Abstract

A superposition rule for two solutions of a Milne--Pinney equation is derived.

14 pages, 2 figures

References in corpus (2)

• Superposition rules, Lie theorem and partial differential equations
• Nonlinear superpositions and Ermakov systems

Cited by in corpus (8)

• Applications of Lie systems in dissipative Milne--Pinney equations
• Mixed superposition rules and the Riccati hierarchy
• Noether symmetries and conservation laws of a reduced gauged bilayer graphene model
• Relativistic Ermakov-Milne-Pinney Systems and First Integrals
• Lie-Hamilton systems on Riemannian and Lorentzian spaces from conformal transformations and some of their applications
• Superposition rules and second-order Riccati equations
• Exact Wave Functions for Generalized Harmonic Oscillators
• Applications of standard and Hamiltonian stochastic Lie systems