5 papers
Integrable tops and non-commutative torus
M. Olshanetsky
We consider the hydrodynamics of the ideal fluid on a 2-torus and its Moyal deformations. The both type of equations have the form of the Euler-Arnold tops. The Laplace operator pl…
Solutions of the periodic Toda lattice via the projection procedure and by the algebra-geometric method
M. Olshanetsky
In this short review we compare different ways to construct solutions of the periodic Toda lattice. We give two recipes that follow from the projection method and compare them with…
W-geometry and Isomonodromic Deformations
M. Olshanetsky
We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked poin…
Painlevé type equations and Hitchin systems
M. Olshanetsky
In this survey we present the interpretation of isomondromy preserving equations on Riemann surfaces with marked points as reduced Hamiltonian systems. The upstairs space is the sp…
The -Fourier transform of -distributions
M. Olshanetsky, V. Rogov
We consider functions on the lattice generated by the integer powers of for and construct the -analog of Fourier transform based on the Jackson integral in the spa…