We define the algebraic variety of almost intertwining matrices to be the set of triples (X,Y,Z) of matrices for which for a 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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© 2001 American Institute of Physics.
2001
American Institute of Physics
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