A new scheme of integrability for (bi)Hamiltonian PDE

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.

35 pages, final version

References in corpus (1)

• Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies

Cited by in corpus (8)

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• Integrable (3+1)-dimensional system with an algebraic Lax pair
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• MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine $\mathcal{W}$-algebras
• Poisson structures in the Banach setting: comparison of different approaches