55 citations · 486 across the 49 of their papers we have counts for
4 papers · 2 filters
Superposition rules for higher-order systems and their applications
J. F. Cariñena, J. Grabowski, J. de Lucas
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular s…
A new Lie systems approach to second-order Riccati equations
J. F. Cariñena, J. de Lucas, C. Sardón
This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations ca…
Lie systems: theory, generalisations, and applications
J. F. Cariñena, J. de Lucas
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular soluti…
Superposition rules and second-order differential equations
J. F. Cariñena, J. de Lucas
The main purpose of this work is to introduce and analyse some generalizations of diverse superposition rules for first-order differential equations to the setting of second-order…