Is my ODE a Painleve equation in disguise?
Exactly Solvable and Integrable Systems
2015-06-26 v1
Abstract
Painleve equations belong to the class y'' + a_1 {y'}^3 + 3 a_2 {y'}^2 + 3 a_3 y' + a_4 = 0, where a_i=a_i(x,y). This class of equations is invariant under the general point transformation x=Phi(X,Y), y=Psi(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 Painleve equations I-IV.
Keywords
Cite
@article{arxiv.nlin/0105016,
title = {Is my ODE a Painleve equation in disguise?},
author = {Jarmo Hietarinta and Valery Dryuma},
journal= {arXiv preprint arXiv:nlin/0105016},
year = {2015}
}
Comments
8 pages. Based on talks presented at NEEDS 2000, Gokova, Turkey, 29 June - 7 July, 2000, and at the AMS-HKMS joint meeting 13-16 December, 2000. Submitted to J. Nonlin. Math. Phys