A geometric approach to integrability conditions for Riccati equations

Abstract

Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.

14 pages

References in corpus (4)

• Riccati equation, Factorization Method and Shape Invariance
• The nonlinear superposition principle and the Wei-Norman method
• Sections along maps in Geometry and Physics
• On some cases of integrability of a general Riccati equation

Cited by in corpus (7)

• Recent Applications of the Theory of Lie Systems in Ermakov Systems
• Quasi-Lie schemes: theory and applications
• Lie families: theory and applications
• Quasi-Lie schemes and Emden--Fowler equations
• Integrability of Lie systems through Riccati equations
• Quasi-Lie schemes for PDEs
• On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation