Journal of Nonlinear Mathematical Physics

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
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - Supplement 1
Pages
110 - 129
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.862438How to use a DOI?
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
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  - https://doi.org/10.1080/14029251.2013.862438
ID  - Kartak2021
ER  -