Poisson pencils: reduction, exactness, and invariants

DOI10.1016/j.geomphys.2018.12.010zbMath1464.37069arXiv1811.11830OpenAlexW2903057337MaRDI QIDQ2416871

Marco Pedroni, Andrea Raimondo, Paolo Lorenzoni

Publication date: 24 May 2019

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.11830

zbMATH Keywords

integrable PDEsDrinfeld-Sokolov reductioncentral invariantsPoisson pencils of hydrodynamic typeexact bi-Hamiltonian manifolds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Poisson manifolds; Poisson groupoids and algebroids (53D17) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Related Items (3)

Algebraic classical \(W\)-algebras and Frobenius manifolds ⋮ Opers for higher states of quantum KdV models ⋮ On integrability of transverse Lie-Poisson structures at nilpotent elements

Cites Work

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• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case
• Deformations of semisimple bihamiltonian structures of hydrodynamic type
• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• On deformation of Poisson manifolds of hydrodynamic type
• On quasi-triviality and integrability of a class of scalar evolutionary PDEs
• Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures
• Lie algebras and equations of Korteweg-de Vries type
• Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
• On Whittaker vectors and representation theory
• Bihamiltonian reductions and \({\mathcal W}_n\)-algebras
• On a linear structure of the quotient variety by a finite reflexion group
• Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures
• Generalized Drinfel'd-Sokolov hierarchies. II: The Hamiltonian structures
• A Darboux theorem for Hamiltonian operators in the formal calculus of variations.
• Compatible flat metrics
• Deformations of bi-Hamiltonian structures of hydrodynamic type
• Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction
• Exact Poisson pencils, \(\tau \)-structures and topological hierarchies
• \(W\)-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions
• Toda theory and \({\mathcal W}\)-algebra from a gauged WZNW point of view
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case
• Compatible Poisson brackets of hydrodynamic type
• THE $W^{(2)}_3$ CONFORMAL ALGEBRA AND THE BOUSSINESQ HIERARCHY
• Deformations of non-semisimple Poisson pencils of hydrodynamic type
• On a certain generator system of the ring of invariants of a finite reflection group
• A note on fractional KdV hierarchies
• An integrable shallow water equation with peaked solitons
• Central invariants revisited
• A Deformation of the Method of Characteristics and the Cauchy Problem for Hamiltonian PDEs in the Small Dispersion Limit
• On Hamiltonian perturbations of hyperbolic systems of conservation laws I: Quasi‐Triviality of bi‐Hamiltonian perturbations

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