A Note on the Poisson Brackets Associated with Lax Operators
نویسنده
چکیده
Modiications of the standard Poisson brackets associated with diierential scattering operators are considered. A linear bracket originates from a non-standard r-matrix on the algebra of pseudo-diierential operators. Two quadratic brackets are investigated which provide Hamiltonian formulations for various reductions of the modiied KP hierarchy.
منابع مشابه
in : Algebraic Aspects of Integrable Systems : In Memory of Irene Dorfman
In remembrance of our dear colleague Irene Dorfman. Abstract Poisson brackets associated with Lax operators of lattice systems are considered. Linear brackets originate from various r-matrices on the algebra of (pseudo-) shift symbols. Quadratic brackets are investigated which provide Hamiltonian formulations for various reductions of the (modiied) Lattice KP hierarchy.
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