Integrability of Lie systems and some of its applications in physics
Jos\'e F. Cari\~nena, Javier de Lucas, Manuel F. Ra\~nada
TL;DR
This paper uses the geometric theory of Lie systems to establish integrability conditions for differential equations like Riccati and Ermakov systems, analyzing various criteria and presenting applications in physics.
Contribution
It introduces a new geometric perspective to analyze integrability of differential equations and compares it with existing criteria, with applications in physics.
Findings
Unified geometric framework for integrability conditions
Analysis of multiple integrability criteria
Applications to physical systems
Abstract
The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analyzed from this new perspective and some applications in physics will be given.
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