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Integrable Systems and Rank One Conditions for Rectangular Matrices

Michael Gekhtman·Alex Kasman
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Abstract

We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices $A$, $B$ and $C$ 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.

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Michael Gekhtman, Alex Kasman. 2004-08-24. Integrable Systems and Rank One Conditions for Rectangular Matrices. https://arxiv.org/abs/math-ph/0408038

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