Equivalence of second-order ODEs to equations of first Painlevé equation type

Authors

  • Yu.Yu. Bagderina
    Institute of Mathematics CC USC RAS, Chernyshevsky str., 112, 450008, Ufa, Russia

DOI:

https://doi.org/10.13108/2015-7-1-19

Keywords:

first Painlevé equation, equivalence, invariant.

Abstract

We consider equivalence problem for equations of a degenerate type, which involve, for example, the first Painlevé equation. In terms of algebraic and differential invariants of the family of equations with the cubic nonlinearity in the first-order derivative, we obtain the necessary condition of equivalence to some equations of this type with a known solution. We prove a criterion of equivalence to the first Painlevé equation under point transformations.

Downloads

Published

20.03.2015