Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy
Exactly Solvable and Integrable Systems
2008-09-17 v2
Abstract
We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy. It allows us to define a matrix Harry Dym hierarchy of commuting Hamiltonian flows in two fields that projects onto the scalar Harry Dym hierarchy. We also show that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.
Keywords
Cite
@article{arxiv.nlin/0612002,
title = {Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy},
author = {Laura Fontanelli and Paolo Lorenzoni and Marco Pedroni and Jorge P. Zubelli},
journal= {arXiv preprint arXiv:nlin/0612002},
year = {2008}
}
Comments
Revised version, 22 pages; a section on reciprocal transformations added. To appear in J. Math. Phys.