Journal of Nonlinear Mathematical Physics

Volume 9, Issue Supplement 1, February 2002, Pages 67 - 74

Is My ODE a Painlevé Equation in Disguise?

Authors
Jarmo Hietarinta, Valery Dryuma
Corresponding Author
Jarmo Hietarinta
Received 8 May 2001, Revised 18 October 2001, Accepted 19 October 2001, Available Online 1 February 2002.
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.6How to use a DOI?
Abstract
Painlevé equations belong to the class y +a1 y 3 +3a2 y 2 +3a3 y +a4 = 0, where ai = ai(x, y). This class of equations is invariant under the general point transformation x = (X, Y ), y = (X, Y ) and it is therefore very difficult to find out whether two equations in this class are related. We describe R. Liouville's theory of invariants that can be used to construct invariant characteristic expressions (syzygies), and in particular present such a characterization for Painlevé equations I-IV.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - Supplement 1
Pages
67 - 74
Publication Date
2002/02/01
ISBN
91-631-2120-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Jarmo Hietarinta
AU  - Valery Dryuma
PY  - 2002
DA  - 2002/02/01
TI  - Is My ODE a Painlevé Equation in Disguise?
JO  - Journal of Nonlinear Mathematical Physics
SP  - 67
EP  - 74
VL  - 9
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s1.6
DO  - https://doi.org/10.2991/jnmp.2002.9.s1.6
ID  - Hietarinta2002
ER  -