Quasi-Lie schemes: theory and applications

Abstract

A powerful method for solving non-linear first-order ordinary differential equations, which is based on geometrical understanding of the corresponding dynamics of the so called Lie systems, is developed. This method allows us not only to solve some of these equations, but also gives a geometrical explanations for some, already known, ad hoc methods of dealing with such problems.

24 pages, major changes in the presentation - the version to be published in J. Phys. A: Math. Theor

References in corpus (7)

• Superposition rules, Lie theorem and partial differential equations
• Recent Applications of the Theory of Lie Systems in Ermakov Systems
• Applications of Lie systems in dissipative Milne--Pinney equations
• A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
• Integrability of Lie systems and some of its applications in physics
• Nonlinear superpositions and Ermakov systems
• A geometric approach to integrability conditions for Riccati equations

Cited by in corpus (13)

• Lie-Hamilton systems on the plane: properties, classification and applications
• Lie--Hamilton systems: theory and applications
• Superposition rules for higher-order systems and their applications
• k-symplectic Lie systems: theory and applications
• Lie families: theory and applications
• Mixed superposition rules and the Riccati hierarchy
• Quasi-Lie schemes and Emden--Fowler equations
• A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
• Lie systems and integrability conditions for t-dependent frequency harmonic oscillators
• Quasi-Lie schemes for PDEs
• Quasi-Lie families, schemes, invariants and their applications to Abel equations
• Superposition rules and second-order Riccati equations
• Stratified Lie systems: Theory and applications