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Solitons and Almost-Intertwining Matrices

Alex Kasman·Michael Gekhtman
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Abstract

We define the set of almost-intertwining matrices to be all triples(X,Y,Z) of n x n matrices for which XZ=YX+T for some rank one matrix T. A surprisingly simple formula is given for tau-functions of the KP hierarchy in terms of such triples. The tau-functions produced in this way include the soliton and vanishing rational solutions. The induced dynamics of the eigenvalues of the matrix X are considered, leading in special cases to the Ruijsenaars-Schneider particle system.

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Alex Kasman, Michael Gekhtman. 2000-11-07. Solitons and Almost-Intertwining Matrices. https://doi.org/10.1063/1.1379313

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