Year: 2026
Type: article
Abstract: We study selected cases of the Hamiltonian of bi-degree (3, 2) with arbitrary analytic coefficients. By imposing constraints on the coefficient functions, which can lower the bi-degree, we can recover the well-known polynomial Hamiltonians with rational coefficients for the Painlevé equations in the regularisation of the corresponding Hamiltonian system. Moreover, for the first and the second Painlevé equations we can also recover polynomial Hamiltonians with meromorphic coefficients. In addition, we examine various shapes of the Newton polygons and graphically visualize the coalescence of the Painlevé equations via inclusion of the Newton polygons into each other.
Author: Galina Filipuk
Institution: University of Warsaw
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7224804164