30 citations · 193 across the 29 of their papers we have counts for
5 papers · 1 filter
Cauchy Biorthogonal Polynomials
M. Bertola, M. Gekhtman, J. Szmigielski
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positiv…
The family of analytic Poisson brackets for the Camassa--Holm hierarchy
M. I. Gekhtman, K. L. Vaninsky
We consider the integrable Camassa--Holm hierarchy on the line with positive initial data rapidly decaying at infinity. It is known that flows of the hierarchy can be formulated in…
On KP Generators and the Geometry of the HBDE
Michael Gekhtman, Alex Kasman
Sato theory provides a correspondence between solutions to the KP hierarchy and points in an infinite dimensional Grassmannian. In this correspondence, flows generated infinitesima…
Integrable Systems and Rank One Conditions for Rectangular Matrices
Michael Gekhtman, Alex Kasman
We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices , and satisfying a rank one condition. This result is…
Solitons and Almost-Intertwining Matrices
Alex Kasman, Michael Gekhtman
We define the set of almost-intertwining matrices to be all triples(X,Y,Z) of n x n matrices for which XZ=YX+T for some rank one matrix T. A surprisingly simple formula is given fo…