Volume 9, Issue Supplement 1, February 2002, Pages 67 - 74
Is My ODE a Painlevé Equation in Disguise?
Jarmo Hietarinta, Valery Dryuma
Received 8 May 2001, Revised 18 October 2001, Accepted 19 October 2001, Available Online 1 February 2002.
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- 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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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 -