Integrable Systems and Rank One Conditions for Rectangular Matrices
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
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 shown to generalize and unify many previous results of different authors on constructions of tau-functions for differential and difference integrable systems from square matrices satisfying rank one conditions. In particular, it contains as explicit special cases the formula of Wilson for tau-functions of rational KP solutions in terms of Calogero-Moser Lax matrices as well as our previous formula for KP tau functions in terms of almost-intertwining matrices.
Cite
@article{arxiv.math-ph/0408038,
title = {Integrable Systems and Rank One Conditions for Rectangular Matrices},
author = {Michael Gekhtman and Alex Kasman},
journal= {arXiv preprint arXiv:math-ph/0408038},
year = {2007}
}