Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies
Functional Analysis
2013-06-06 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We propose a method for computing any Gelfand-Dickey tau function living in Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols. Also truncated block Toeplitz determinants associated to the same symbols are shown to be tau function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.
Keywords
Cite
@article{arxiv.0711.2248,
title = {Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies},
author = {Mattia Cafasso},
journal= {arXiv preprint arXiv:0711.2248},
year = {2013}
}
Comments
35 pages. Typos corrected, some changes in the introduction