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
- 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/).
Cite this article
TY - JOUR AU - Vera V. Kartak PY - 2021 DA - 2021/01/07 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 - 10.1142/S1402925111001799 ID - Kartak2021 ER -