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. © 2008 American Institute of Physics.
Fontanelli, L., Lorenzoni, P., Pedroni, M., Zubelli, J. (2008). Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy. JOURNAL OF MATHEMATICAL PHYSICS, 49(9), 092901 [10.1063/1.2982232].
Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy
LORENZONI, PAOLO;
2008
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. © 2008 American Institute of Physics.
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