It is shown that all stationary and restricted flows of the Harry-Dym hierarchy have a parametrization as a set of Newton equations. They are new classes of integrable mechanical systems. Properties of the Harry-Dym hierarchy are used for deriving systematically spectral-parameter-dependent Lax representations and bi-Hamiltonian formulation for some of these systems. They yield complete sets of integrals in involution which render these systems to be completely integrable.
Ragnisco, O., Rauchwojciechowski, S. (1994). INTEGRABLE MECHANICAL SYSTEMS RELATED TO THE HARRY-DYM HIERARCHY. JOURNAL OF MATHEMATICAL PHYSICS, 35(2), 834-847 [10.1063/1.530616].
INTEGRABLE MECHANICAL SYSTEMS RELATED TO THE HARRY-DYM HIERARCHY
RAGNISCO, Orlando;
1994-01-01
Abstract
It is shown that all stationary and restricted flows of the Harry-Dym hierarchy have a parametrization as a set of Newton equations. They are new classes of integrable mechanical systems. Properties of the Harry-Dym hierarchy are used for deriving systematically spectral-parameter-dependent Lax representations and bi-Hamiltonian formulation for some of these systems. They yield complete sets of integrals in involution which render these systems to be completely integrable.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
