7 papers · 1 filter
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…
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…
KP Solitons are Bispectral
Alex Kasman
It is by now well known that the wave functions of rational solutions to the KP hierarchy which can be achieved as limits of the pure -soliton solutions satisfy an eigenvalue eq…
Darboux Transformations of Bispectral Quantum Integrable Systems
Emil Horozov, Alex Kasman
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differen…