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arXiv · 0902.2132

Applications of Lie systems in dissipative Milne--Pinney equations

J. F. Cariñena·J. de Lucas
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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.

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J. F. Cariñena, J. de Lucas. 2009-02-12. Applications of Lie systems in dissipative Milne--Pinney equations. https://doi.org/10.1142/s0219887809003758

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