Lie point symmetries and ODEs passing the Painlevé test
- 10.1080/14029251.2018.1503435How to use a DOI?
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 PIII, PV and PVI 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.
- © 2018 The Authors. Published by Atlantis and Taylor & Francis
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- 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 - 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 -