Solitons and Almost-Intertwining Matrices
Mathematical Physics
2009-10-31 v1 math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.math-ph/0011011,
title = {Solitons and Almost-Intertwining Matrices},
author = {Alex Kasman and Michael Gekhtman},
journal= {arXiv preprint arXiv:math-ph/0011011},
year = {2009}
}