Lie point symmetry analysis of a second order differential equation with singularity

Abstract

Listen

Translate article

By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov–Pinney equation. In this context, nonlinear superposition rule for second order Kummer–Schwarz equation is rediscovered. Invariance under one-dimensional symmetry group is also used to obtain first integrals (Ermakov–Lewis invariants). Our motivation is a type of equations with singular term that arises in many applications, in particular in the study of general NLS (nonlinear Schrödinger) equations.