The Frobenius-Virasoro algebra and Euler equations

DOI10.1016/j.geomphys.2014.08.002zbMath1304.35627arXiv1403.0027OpenAlexW2053257495MaRDI QIDQ478835

Dafeng Zuo

Publication date: 4 December 2014

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

Full work available at URL: https://arxiv.org/abs/1403.0027

zbMATH Keywords

Euler equationsHunter-Saxton equationFrobenius algebraCamassa-Holm equation (CM)Frobenius-Virasoro algebraKorteweg-de Vries equation (KdV)

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) KdV equations (Korteweg-de Vries equations) (35Q53) Euler equations (35Q31)

Related Items (12)

Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy ⋮ A new class of Euler equation on the dual of the N = 1 extended Neveu-Schwarz algebra ⋮ Frobenius manifolds and Frobenius algebra-valued integrable systems ⋮ Free-field realizations of the W_{𝒜 n , N} -algebra ⋮ Super Camassa–Holm-type systems associated to the Kuper–Ramond–Schwarz superalgebra ⋮ A kind of generalized integrable couplings and their bi-Hamiltonian structure ⋮ The Frobenius-Virasoro algebra and Euler equations. II: Multi-component cases ⋮ A kind of nonisospectral and isospectral integrable couplings and their Hamiltonian systems ⋮ Supersymmetric Euler equations associated to the N ≤ 3 Neveu-Schwarz algebra ⋮ Residual symmetries and Bäcklund transformations of \((2+1)\)-dimensional strongly coupled Burgers system ⋮ A new multi-component integrable coupling and its application to isospectral and nonisospectral problems ⋮ Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)^th KdV Hierarchy

Cites Work

• Unnamed Item
• Multi-component integrable systems and invariant curve flows in certain geometries
• Euler equations related to the generalized Neveu-Schwarz algebra
• Bäcklund transformations for new integrable hierarchies related to the polynomial Lie algebra \(\mathfrak{gl}_{\infty}^{(n)}\)
• Classical r-matrices and compatible Poisson brackets for coupled KdV systems
• Korteweg - de Vries suoerequation as an Euler equation
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Topological methods in hydrodynamics
• Euler equations on homogeneous spaces and Virasoro orbits
• Frobenius manifolds and Frobenius algebra-valued integrable systems
• Geodesic flow and two (super) component analog of the Camassa-Holm equation
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• New integrable hierarchies from vertex operator representations of polynomial Lie algebras
• Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations
• Bihamiltonian Equations on Polynomial Virasoro
• A two-component μ-Hunter–Saxton equation
• The Geometry of Infinite-Dimensional Groups
• Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations

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