On some examples of identifying Painlevé equations using the geometry of the Okamoto space of initial conditions

2025/08/16 by Dzhamay, Anton
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.12052

Abstract

In this short note we give two examples of using the algebro-geometric theory of Painlevé equations to solve the Painlevé identification problem. The equations that we consider were recently obtained by M. van der Put and J. Top in their study of a certain ansatz of isomonodromic deformations of linear ODEs. We provide explicit coordinate transformations identifying these examples with standard form of some Painlevé equations and also explicitly identify their Hamiltonians.

Citations

• Isomonodromy and Painlevé Type Equations, Case Studies

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