Lie systems and integrability conditions of differential equations and some of its applications
J.F. Cari\~nena, J. de Lucas
TL;DR
This paper uses the geometric theory of Lie systems to derive integrability conditions for various differential equations, including Riccati and Ermakov systems, and explores their applications in physics.
Contribution
It introduces a new geometric perspective to analyze integrability criteria and unifies various existing conditions within the Lie systems framework.
Findings
Derived new integrability conditions for Riccati and Ermakov systems
Analyzed existing criteria through Lie systems perspective
Presented applications of these conditions in physics
Abstract
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analysed from this new perspective, and some applications in physics will be given.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Advanced Algebra and Geometry