Applications of Lie systems in dissipative Milne--Pinney equations

Abstract

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne--Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.

To be published in the Int. J. Geom. Methods Mod. Phys

References in corpus (2)

• Superposition rules, Lie theorem and partial differential equations
• A nonlinear superposition rule for solutions of the Milne--Pinney equation

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