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

F. Güngör; P. J. Torres

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arXiv · 1612.07080

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

F. Güngör·P. J. Torres

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Abstract

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 Schr\"odinger) equations.

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F. Güngör, P. J. Torres. 2016-12-21. Lie point symmetry analysis of a second order differential equation with singularity. https://arxiv.org/abs/1612.07080

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