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math-ph2000★ 24 cited
Solitons and Almost-Intertwining Matrices
Alex Kasman, Michael Gekhtman
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 fo…
nlin.SI2000
Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices
L. Faybusovich, M. Gekhtman
We introduce a family of compatible Poisson brackets on the space of rational functions with denominator of a fixed degree and use it to derive a multi-Hamiltonian structure for a…
nlin.SI2000
On billiard weak solutions of nonlinear PDE's and Toda flows
Mark Alber, Roberto Camassa, Michael Gekhtman
A certain class of partial differential equations possesses singular solutions having discontinuous first derivatives ("peakons"). The time evolution of peaks of such solutions is…