58 citations · 279 across the 24 of their papers we have counts for
9 papers · 1 filter
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…
On the Quantization of a Self-Dual Integrable System
Alex Kasman
In this note, we apply canonical quantization to the self-dual particle system describing the motion of poles to a higher rank solution of the KP hierarchy, explicitly determining…
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…
Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations
Alex Kasman
Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rati…
Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
Alex Kasman
A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of…