Invariant differential equations and the Adler–Gel’fand–Dikii bracket

DOI10.1063/1.532162zbMath0892.58037arXivhep-th/9603199OpenAlexW3104054625MaRDI QIDQ4378318

Rafael Hernández Heredero, Artemio González-López, Gloria Marí Beffa

Publication date: 27 July 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9603199

zbMATH Keywords

Adler-Gel'fand-Dikij bracketssecond Hamiltonian KdV structures

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (10)

Large chiral diffeomorphisms on Riemann surfaces and W-algebras ⋮ Integrable motions of curves in \(S^{1} \times \mathbb R\) ⋮ Euler-Poincaré flows on \(\mathrm{sl}_{ n }\) opers and integrability ⋮ On generalizations of the pentagram map: discretizations of AGD flows ⋮ SPACE OF HIGHER ORDER DIFFERENTIAL OPERATORS ON S¹ AND INTEGRABLE FLOWS ⋮ Antiplectic structure, diffeomorphism and generalized KdV family ⋮ The theory of differential invariants and KDV hamiltonian evolutions ⋮ Remarks on KdV-type flows on star-shaped curves ⋮ ON THE GEOMETRY OF STAR-SHAPED CURVES IN R<i>ⁿ</i> ⋮ Diffeomorphisms on S¹, projective structures and integrable systems

Cites Work

• Symplectic leaves of the Gel'fand-Dikij brackets and homotopy classes of nondegenerate curves
• Lie algebras and equations of Korteweg-de Vries type
• 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
• On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket
• SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type

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