The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure

DOI10.1007/s40879-019-00329-4zbMath1442.37083OpenAlexW2930342612WikidataQ128127545 ScholiaQ128127545MaRDI QIDQ1987711

Yanyan Li

Publication date: 15 April 2020

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40879-019-00329-4

zbMATH Keywords

Casimir invariantsAdler-Kostant-Symes theoryintegrable heavenly equationsLax-Sato integrabilitysuper-conformal vector fields

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) PDEs in connection with relativity and gravitational theory (35Q75) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Analysis on supermanifolds or graded manifolds (58C50) Einstein equations (35Q76)

Related Items (2)

Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics

Cites Work

• Unnamed Item
• Unnamed Item
• Linearly degenerate partial differential equations and quadratic line complexes
• Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems
• Superanalysis, I. Differential calculus
• Integrable dispersionless PDEs in 4D, their symmetry pseudogroups and deformations
• Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
• On the Hamiltonian formalism for Korteweg-de Vries type hierarchies
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Geometric structure of the classical Lagrange-d'Alembert principle and its application to integrable nonlinear dynamical systems
• Lie algebras of differential operators, their central extensions, and W- algebras
• Looped cotangent Virasoro algebra and nonlinear integrable systems in dimension \(2+1\)
• Recursion operators and bi-Hamiltonian structure of the general heavenly equation
• Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle
• Hydrodynamic reductions and solutions of a universal hierarchy
• Einstein–Weyl geometry, dispersionless Hirota equation and Veronese webs
• On the Einstein-Weyl and conformal self-duality equations
• Lax-integrable Laberge–Mathieu hierarchy of supersymmetric nonlinear dynamical systems and its finite-dimensional reduction of Neumann type
• Compatibly bi-Hamiltonian superconformal analogs of Lax-integrable nonlinear dynamical systems
• Bi-Hamiltonian nature of the equation utx = uxyuy – uyyux
• Integrable hydrodynamic chains
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Grassmannians Gr(N− 1, N+ 1), closed differentialN− 1-forms andN-dimensional integrable systems
• Linearly degenerate hierarchies of quasiclassical SDYM type
• Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

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