128 citations · 447 across the 39 of their papers we have counts for
14 papers · 1 filter
Monge-Ampere Geometry and Vortices
Lewis Napper, Ian Roulstone, Vladimir Rubtsov +1
We introduce a new approach to Monge-Ampere geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge-Ampere geometry to the P…
Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds
Roberto D'Onofrio, Giovanni Ortenzi, Ian Roulstone +1
Using Monge-Ampère geometry, we study the singular structure of a class of nonlinear Monge-Ampère equations in three dimensions, arising in geophysical fluid dynamics. We extend se…
A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions
Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov +1
We study a fully noncommutative generalisation of the commutative fourth Painlevé equation that possesses solutions in terms of an infinite Toda system over an associative unital d…
On the Kadomtsev-Petviashvili hierarchy in an extended class of formal pseudo-differential operators
Jean-Pierre Magnot, Vladimir Rubtsov
We study the existence and uniqueness of the Kadomtsev-Petviashvili (KP) hierarchy solutions in the algebra of $\F Cl(S^1,\K^n)$ of formal classical pseudo-differential operators.…
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…
Noncommutative Painlevé equations and systems of Calogero type
Marco Bertola, Mattia Cafasso, Vladimir Roubtsov
All Painlevé equations can be written as a time-dependent Hamiltonian system, and as such they admit a natural generalization to the case of several particles with an interaction o…