128 citations · 447 across the 39 of their papers we have counts for
42 papers
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…
Frolicher structures, diffieties, and a formal KP hierarchy
Jean-Pierre Magnot, Enrique G. Reyes, Vladimir Rubtsov
We propose a definition of a diffiety based on the theory of Frolicher structures. As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existe…
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 Zakharov-Shabat equations of generalized Kadomtsev-Petviashvili hierarchies
Jean-Pierre Magnot, Enrique G. Reyes, Vladimir Rubtsov
We review the integration of the KP hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped…
Isomonodromic deformations: Confluence, Reduction Quantisation
Ilia Gaiur, Marta Mazzocco, Vladimir Rubtsov
In this paper we study the isomonodromic deformations of systems of differential equations with poles of any order on the Riemann sphere as Hamiltonian flows on the product of co-a…