Integrability of Lie systems and some of its applications in physics

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.

16 pages

References in corpus (2)

• Superposition rules, Lie theorem and partial differential equations
• Nonlinear superpositions and Ermakov systems

Cited by in corpus (5)

• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• Quasi-Lie schemes and Emden--Fowler equations
• A geometric approach to time evolution operators of Lie quantum systems
• A Lie systems approach for the first passage-time of piecewise deterministic processes
• Superposition rules and second-order Riccati equations