A New Scheme of Integrability for (bi)Hamiltonian PDE
Author(s)
De Sole, Alberto; Kac, Victor G; Valeri, Daniele
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© 2016, Springer-Verlag Berlin Heidelberg. 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.
Date issued
2016Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Communications in Mathematical Physics
Publisher
Springer Nature America, Inc
Citation
De Sole, Alberto, Victor G. Kac, and Daniele Valeri. "A New Scheme of Integrability for (Bi)Hamiltonian Pde." Communications in Mathematical Physics 347 2 (2016): 449-88.
Version: Author's final manuscript