title: |
Is My ODE a Painlevé Equation in Disguise? |
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publication: |
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| volume-issue: | 9 - Supplement 1 | |
| pages: | 67 - 74 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2002.9.s1.6 (how to use a DOI) | |
author(s): |
Jarmo HIETARINTA, Valery DRYUMA |
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publication date: |
February 2002 |
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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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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |