Journal of Nonlinear Mathematical Physics

Volume 18, Issue 1, March 2011, Pages 29 - 54

Integrability of Lie Systems through Riccati Equations

Authors
José F. Cariñena
Departamento de Física Teórica, Universidad de Zaragoza, c. Pedro Cerbuna 12, Zaragoza, 50.009, Spain, jfc@unizar.es
Javier de Lucas
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, Warszawa, P.O. Box 21, 00-596, Poland, delucas@impan.pl
Received 27 January 2010, Accepted 13 May 2010, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925111001131How to use a DOI?
Keywords
Lie–Scheffers systems, Riccati equations, integrability conditions
Abstract

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyze a geometric method to construct integrability conditions for Riccati equations following these approaches. Our procedure provides us with a unified geometrical viewpoint that allows us to analyze some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalized to describe integrability conditions for any Lie system. Finally we show the usefulness of our treatment in order to study the problem of the linearizability of Riccati equations.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 1
Pages
29 - 54
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925111001131How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - José F. Cariñena
AU  - Javier de Lucas
PY  - 2021
DA  - 2021/01
TI  - Integrability of Lie Systems through Riccati Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 29
EP  - 54
VL  - 18
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001131
DO  - https://doi.org/10.1142/S1402925111001131
ID  - Cariñena2021
ER  -