English

Applications of Lie systems in dissipative Milne--Pinney equations

Mathematical Physics 2009-10-03 v1 math.MP

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.

Keywords

Cite

@article{arxiv.0902.2132,
  title  = {Applications of Lie systems in dissipative Milne--Pinney equations},
  author = {J. F. Cariñena and J. de Lucas},
  journal= {arXiv preprint arXiv:0902.2132},
  year   = {2009}
}

Comments

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