Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations

DOI10.1111/sapm.12040zbMath1301.35139arXiv1309.3188OpenAlexW3125913502MaRDI QIDQ2925252

Błażej M. Szablikowski, Ian A. B. Strachan

Publication date: 21 October 2014

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3188

zbMATH Keywords

Euler equationsKorteweg-de VriesNovikov algebrasCamassa-Holm-type equationsmulticomponent integrable systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Applications of Lie algebras and superalgebras to integrable systems (17B80) Nonassociative algebras satisfying other identities (17A30) Soliton solutions (35C08) Euler equations (35Q31)

Related Items (24)

The WDVV associativity equations as a high-frequency limit ⋮ Hamilton Operators and Related Integrable Differential Algebraic Novikov–Leibniz Type Structures ⋮ 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 ⋮ Projective-geometric aspects of bi-Hamiltonian structures of KdV type ⋮ Liouville correspondences between multicomponent integrable hierarchies ⋮ Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures ⋮ Two-component generalizations of the Camassa–Holm equation ⋮ Bi-Hamiltonian structures of KdV type ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies, and multicomponent Hunter-Saxton equations ⋮ The Frobenius-Virasoro algebra and Euler equations ⋮ Non-associative structures of commutative algebras related with quadratic Poisson brackets ⋮ The Frobenius-Virasoro algebra and Euler equations. II: Multi-component cases ⋮ On finite dimensional simple Novikov superalgebras ⋮ Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation ⋮ Integrable systems, multicomponent twisted Heisenberg-Virasoro algebra and its central extensions ⋮ Projective-geometric aspects of homogeneous third-order Hamiltonian operators ⋮ Bi-Hamiltonian systems in \((2+1)\) and higher dimensions defined by Novikov algebras ⋮ Supersymmetric Euler equations associated to the N ≤ 3 Neveu-Schwarz algebra ⋮ Remarks on certain two-component systems with peakon solutions ⋮ Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators ⋮ Conserved quantities, continuation and compactly supported solutions of some shallow water models

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