Integrability of Lie systems through Riccati equations

Details Integrability of Lie systems through Riccati equations Integrability of Lie systems through Riccati equations

2010-02-02

arxiv.org/abs/1002.0530v3

J. Nonlinear Math. Phys. 18 (1), 29--54 (2011)

Physics

Mathematical Physics

Corrected typos

Scientific paper

10.1142/S1402925111001131

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.

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