Painleve Test and the Resolution of Singularities for Integrable Equations
Classical Analysis and ODEs
2013-05-01 v1
Abstract
We prove that under a very general setting, a system of ODE passes the Painleve test if and only if there is a good change of variable, such that the pole singularity solutions are converted to regular power series, while the converted ODE system is still kept regular. A consequence is that all principal balances of an ODE system converge. We also prove that the results are natural with respect to Hamiltonian systems.
Keywords
Cite
@article{arxiv.1304.7982,
title = {Painleve Test and the Resolution of Singularities for Integrable Equations},
author = {Jishan Hu and Min Yan},
journal= {arXiv preprint arXiv:1304.7982},
year = {2013}
}