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Equivalence Problem of the Painlevé Equations
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand
- 1 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand
Advances in Pure Mathematics·Volume 03 (2013)·Pages 297–303·Published 5 March 2013·DOI10.4236/apm.2013.32042
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Abstract
The manuscript is devoted to the equivalence problem of the Painlevé equations. Conditions which are necessary and sufficient for second-order ordinary differential equations y ″ =F ( x ,y, y ′ ) to be equivalent to the first and second Painlevé equation under a general point transformation are obtained. A procedure to check these conditions is found.
KeywordsEquivalence ProblemPainlevéEquationsPoint Transformation
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