Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures

DOI10.1007/s12220-023-01237-6zbMath1518.37070arXiv2112.09471OpenAlexW4366185771MaRDI QIDQ6157813

Andrey Yu. Konyaev, Alexei V. Bolsinov, Vladimir S. Matveev

Publication date: 12 May 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.09471

zbMATH Keywords

Frobenius algebrasNijenhuis operatorscompatible Poisson bracketsdispersive perturbationdifferential geometric Poisson bracketsintegrable PDE systems

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) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Related Items (6)

Projective geometry of homogeneous second-order Hamiltonian operators ⋮ Nijenhuis geometry. III: \(\mathrm{gl}\)-regular Nijenhuis operators ⋮ Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems ⋮ Elementary differential singularities of three-dimensional Nijenhuis operators ⋮ Integrating Nijenhuis structures ⋮ Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies, and multicomponent Hunter-Saxton equations

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