Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies

Details Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies

2007-11-14

arxiv.org/abs/0711.2248v2

Mathematics

Functional Analysis

35 pages. Typos corrected, some changes in the introduction

Scientific paper

10.1007/s11040-008-9038-7

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.

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