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Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy

Laura Fontanelli·Paolo Lorenzoni·Marco Pedroni·Jorge P. Zubelli
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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.

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Laura Fontanelli, Paolo Lorenzoni, Marco Pedroni, Jorge P. Zubelli. 2008-09-17. Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy. https://arxiv.org/abs/nlin/0612002

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