2 papers
math-ph2020
Dualities for rational multi-particle Painlevé systems: Spectral versus Ruijsenaars
Ilia Gaiur, Vladimir Rubtsov
The extension of the Painlevé-Calogero coorespondence for n-particle Inozemtsev systems raises to the multi-particle generalisations of the Painlevé equations which may be obtained…
math.CA2019
Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations
Dmitry I. Sinelshchikov, Ilia Yu. Gaiur, Nikolay A. Kudryashov
We consider a family of non-autonomous second-order differential equations, which generalizes the Liénard equation. We explicitly find the necessary and sufficient conditions for m…