On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket

DOI10.1088/0951-7715/5/1/004zbMath0761.58023OpenAlexW2093189898MaRDI QIDQ3990942

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Publication date: 28 June 1992

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/5/1/004

zbMATH Keywords

loop groupsAdler-Gel'fand-Dikii bracketantiplectic formalismcomposition of ordinary differential operators

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Loop groups and related constructions, group-theoretic treatment (22E67) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Hamiltonian and Lagrangian mechanics (70H99) Ordinary differential operators (34L99) General models, approaches, and methods in mechanics of particles and systems (70G99)

Related Items (11)

Canonical property of the Miura maps between the MKP and KP hierarchies, continuous and discrete ⋮ Integral operators, bispectrality and growth of Fourier algebras ⋮ Algebras of commuting differential operators for kernels of Airy type ⋮ Darboux-Bäcklund solutions of \(\text{SL}(p,q)\) KP-KdV hierarchies, constrained generalized Toda lattices, and two-matrix string model ⋮ Invariant differential equations and the Adler–Gel’fand–Dikii bracket ⋮ Euler-Poincaré flows and Leibniz structure of nonlinear reaction-diffusion type systems ⋮ Antiplectic structure, diffeomorphism and generalized KdV family ⋮ Poisson groups and differential Galois theory of Schrödinger equation on the circle ⋮ The theory of differential invariants and KDV hamiltonian evolutions ⋮ On Grassmannian description of the constrained KP hierarchy ⋮ Diffeomorphisms on S¹, projective structures and integrable systems

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