We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

A new scheme of integrability for (bi)Hamiltonian PDE / DE SOLE, Alberto; Kac, Victor G.; Valeri, Daniele. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 347:2(2016), pp. 449-488. [10.1007/s00220-016-2684-x]

A new scheme of integrability for (bi)Hamiltonian PDE

DE SOLE, ALBERTO;Valeri, Daniele
2016

Abstract

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.
2016
statistical and nonlinear physics; mathematical physics
01 Pubblicazione su rivista::01a Articolo in rivista
A new scheme of integrability for (bi)Hamiltonian PDE / DE SOLE, Alberto; Kac, Victor G.; Valeri, Daniele. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 347:2(2016), pp. 449-488. [10.1007/s00220-016-2684-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/972800
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