Halphen's Transform for the Lamé Equation and Ermakov–Painlevé XXV Equation
Galina Filipuk, Alexander Chichurin
Source abstract
ABSTRACT In S. Reiter (J. reine angew. Math. 704, 2015) it was shown that the Halphen transform of a Lamé equation can be written as the symmetric square of this equation followed by an Euler transformation via third‐order linear differential equations. In this paper, we examine nonlinear second‐order differential equations, which are associated to the third‐order linear differential equations via the Schwarzian derivative, and determine whether they are reduced to either the Ermakov equation or to the Painlevé XXV equation.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.