Lie point symmetries and ODEs passing the Painlevé test

DOI

10.1080/14029251.2018.1503435How to use a DOI?

Abstract

The Lie point symmetries of ordinary differential equations (ODEs) that are candidates for having the Painlevé property are explored for ODEs of order n = 2, . . . , 5. Among the 6 ODEs identifying the Painlevé transcendents only P_III, P_V and P_VI have nontrivial symmetry algebras and that only for very special values of the parameters. In those cases the transcendents can be expressed in terms of simpler functions, i.e. elementary functions, solutions of linear equations, elliptic functions or Painlevé transcendents occurring at lower order. For higher order or higher degree ODEs that pass the Painlevé test only very partial classifications have been published. We consider many examples that exist in the literature and show how their symmetry groups help to identify those that may define genuinely new transcendents.

Copyright

© 2018 The Authors. Published by Atlantis 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/).

Download article (PDF)
View full text (HTML)

TY  - JOUR
AU  - D. Levi
AU  - D. Sekera
AU  - P. Winternitz
PY  - 2021
DA  - 2021/01/06
TI  - Lie point symmetries and ODEs passing the Painlevé test
JO  - Journal of Nonlinear Mathematical Physics
SP  - 604
EP  - 617
VL  - 25
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1503435
DO  - 10.1080/14029251.2018.1503435
ID  - Levi2021
ER  -