56 citations · 289 across the 35 of their papers we have counts for
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Generalisation of Bureau-Guillot systems with Painlevé transcendents in the coefficients
Marta Dell'Atti, Galina Filipuk
We construct a generalisation of what we call Bureau-Guillot systems, i.e. systems of first order equations with coefficient functions being Painlevé transcendents. The same Painle…
Iterative polynomial regularisation of PIV-type: Hamiltonian systems and Newton polygons
Marta Dell'Atti, Galina Filipuk
We study several polynomial Hamiltonian systems of PIV-type (including the mixed case quasi-PIV), and show that via the iterative process of polynomial regularisation, it is possib…
Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric approach and birational equivalence
Marta Dell'Atti, Galina Filipuk
Bureau proposed a classification of systems of quadratic differential equations in two variables which are free of movable critical points, which was recently revised by Guillot. W…
On the solutions of the critical Lane-Emden equation in higher space dimensions
Radoslaw Antoni Kycia, Galina Filipuk
In this paper we study solutions of the critical Lane-Emden equation in higher space dimensions. We show that after certain transformations the general solution can be written in t…