Integrable Systems and Rank One Conditions for Rectangular Matrices

Details Integrable Systems and Rank One Conditions for Rectangular Matrices Integrable Systems and Rank One Conditions for Rectangular Matrices

2004-08-24

arxiv.org/abs/math-ph/0408038v1

Theoretical and Mathematical Physics 133(2): 1498-1503 (2002)

Physics

Mathematical Physics

Scientific paper

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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