TITLE:
Equivalence Problem of the Painlevé Equations
AUTHORS:
Sopita Khamrod
KEYWORDS:
Equivalence Problem; Painlevé Equations; Point Transformation
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.2,
March
19,
2013
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.