Applications of Lie systems in dissipative Milne--Pinney equations

Details Applications of Lie systems in dissipative Milne--Pinney equations Applications of Lie systems in dissipative Milne--Pinney equations

2009-02-12

arxiv.org/abs/0902.2132v1

International Journal of Geometric Methods in Modern Physics, vol. 06, issue 04, p. 683 (2009).

Physics

Mathematical Physics

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

Scientific paper

10.1142/S0219887809003758

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.

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