Explicit solutions of the ${\mathfrak{a}}_1$-type Lie-Scheffers system and a general Riccati equation

Abstract

For a general differential system $\dot{x}(t)={\sum }_{d=1}^3{u}_d(t)X_d$, where $X_d$ generates the simple Lie algebra of type ${\mathfrak{a}}_1$, we compute the explicit solution in terms of iterated integrals of products of $u_d$'s. As a byproduct we obtain the solution of a general Riccati equation by infinite quadratures.

16 pages. The final publication is available at link.springer.com

References in corpus (3)

• Recent Applications of the Theory of Lie Systems in Ermakov Systems
• Applications of Lie systems in dissipative Milne--Pinney equations
• Integrability of Lie systems through Riccati equations

Cited by in corpus (3)

• k-symplectic Lie systems: theory and applications
• On Lie systems and Kummer-Schwarz equations
• A Quasi-Lie Schemes Approach to Second-Order Gambier Equations