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arXiv · 1304.7982

Painleve Test and the Resolution of Singularities for Integrable Equations

Jishan Hu·Min Yan
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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.

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BibTeXRIS

Jishan Hu, Min Yan. 2013-04-30. Painleve Test and the Resolution of Singularities for Integrable Equations. https://arxiv.org/abs/1304.7982

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