Equivalence Problem of the Painlevé Equations

Sopita Khamrod

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand.

DOI: 10.4236/apm.2013.32042                

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.

Keywords

Equivalence Problem; Painlevé Equations; Point Transformation

Conflicts of Interest

The authors declare no conflicts of interest.

References

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