Families of quai-bi-Hamiltonian systems and separability

Details Families of quai-bi-Hamiltonian systems and separability Families of quai-bi-Hamiltonian systems and separability

1999-06-10

arxiv.org/abs/solv-int/9906005v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, Amstex, no figues, to be published in Journal of Mathematical Physics

Scientific paper

It is shown how to construct an infinite number of families of quasi-bi-Hamiltonian (QBH) systems by means of the constrained flows of soliton equations. Three explicit QBH structures are presented for the first three families of the constrained flows. The Nijenhuis coordinates defined by the Nijenhuis tensor for the corresponding families of QBH systems are proved to be exactly the same as the separated variables introduced by means of the Lax matrices for the constrained flows.

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