Journal of Nonlinear Mathematical Physics

Volume 18, Issue 4, December 2011, Pages 613 - 640

Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant

Authors
Vera V. Kartak
Chair of Higher Algebra and Geometry, Faculty of Mathematics and Information Technologies, Bashkir State University, ul. Z.Validi, 32, Ufa, 450074, Russia, kvera@mail.ru
Received 17 November 2010, Accepted 20 August 2011, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925111001799How to use a DOI?
Keywords
Invariant, equivalence problem, ordinary differential equation, point transformation, Painleve equation, Emden equation
Abstract

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the examples the equivalence problem for the Painleve II equation, Painleve III equation with three zero parameters, Emden equations and for some other equations is solved.

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 - 4
Pages
613 - 640
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925111001799How 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  - Vera V. Kartak
PY  - 2021
DA  - 2021/01
TI  - Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant
JO  - Journal of Nonlinear Mathematical Physics
SP  - 613
EP  - 640
VL  - 18
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001799
DO  - https://doi.org/10.1142/S1402925111001799
ID  - Kartak2021
ER  -