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The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. (English) Zbl 0678.70015

Summary: A new approach to Hamiltonian structures of integrable systems is proposed by making use of a trace identity. For a variety of isospectral problems that can be unified to one model \(\psi_ x=U\psi\), it is shown that both the related hierarchy of evolution equations and the Hamiltonian structure can be obtained from the same solution of the equation \(V_ x=[U,V]\).

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
70H05 Hamilton’s equations
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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