The theory of differential invariants and KDV hamiltonian evolutions

DOI10.24033/bsmf.2353zbMath1053.37046OpenAlexW943352514MaRDI QIDQ4700607

Gloria Marí Beffa

Publication date: 4 November 1999

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1999__127_3_363_0

zbMATH Keywords

differential invariantsprojective actionAdler-Gel'fand-Dikii Poisson bracketsinvariant evolutions of projective curvesKdV Hamiltonian evolutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Differential invariants (local theory), geometric objects (53A55)

Related Items (10)

Integrable motions of curves in \(S^{1} \times \mathbb R\) ⋮ On generalizations of the pentagram map: discretizations of AGD flows ⋮ Unnamed Item ⋮ Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces ⋮ Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces ⋮ Poisson brackets associated to the conformal geometry of curves ⋮ Evolution of curvature invariants and lifting integrability ⋮ Hamiltonian evolution of curves in classical affine geometries ⋮ A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms ⋮ Remarks on KdV-type flows on star-shaped curves

Cites Work

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• Modifying Lax equations and the second Hamiltonian structure
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Differential invariants for parametrized projective surfaces
• ON ANTIPLECTIIC PAIRS IN THE HAMILITONIAN FORMALISM OF EVOLUTION EQUATIONS
• On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket
• Invariant differential equations and the Adler–Gel’fand–Dikii bracket
• SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type

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