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arXiv · 0711.2248

Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies

Mattia Cafasso
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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.

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BibTeXRIS

Mattia Cafasso. 2007-11-25. Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies. https://doi.org/10.1007/s11040-008-9038-7

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