Volume 20, Issue Supplement 1, November 2013, Pages 110 - 129
Point classification of second order ODEs and its application to Painlevé equations
Authors
Vera V. Kartak
Chair of Higher Algebra and Geometry, Faculty of Mathematics and Information Technologies, Bashkir State University, Z.Validi Str., 32, Ufa, 450074, Russia
Laboratory ”Group analysis of mathematical models in natural and engineering sciences”, Ufa State Aviation Technical University, 12, K. Marx Str., Ufa, 450000, Russia,kvera@mail.ru
Received 9 July 2012, Accepted 28 May 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.862438How to use a DOI?
- Keywords
- Invariant; Problem of equivalence; Point transformation; Painlevé equation
- Abstract
The first part of this work is a review of the point classification of second order ODEs done by Ruslan Sharipov. His works were published in 1997–1998 in the Electronic Archive at LANL. The second part is an application of this classification to Painlevé equations. In particular, it allows us to solve the equivalence problem for Painlevé equations in an algorithmic form.
- Copyright
- © 2013 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 - Vera V. Kartak PY - 2021 DA - 2021/01/06 TI - Point classification of second order ODEs and its application to Painlevé equations JO - Journal of Nonlinear Mathematical Physics SP - 110 EP - 129 VL - 20 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.862438 DO - 10.1080/14029251.2013.862438 ID - Kartak2021 ER -