Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics

DOI10.3842/SIGMA.2019.079zbMath1460.17040arXiv1902.08111MaRDI QIDQ2330856

Oksana Ye. Hentosh, Anatoliy K. Prykarpatsky, Yarema A. Prykarpatsky, D. L. Blackmore

Publication date: 23 October 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08111

zbMATH Keywords

Hamiltonian systemLie-Poisson structureLax integrabilityCasimir invariantsconformal structuresLie-algebraic schemeLax-Sato equationsloop Lie algebratorus diffeomorphisms\(R\)-structuremulti-dimensional heavenly equationsmulti-dimensional integrable heavenly equations

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) 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) Invariance and symmetry properties for PDEs on manifolds (58J70) Applications of Lie algebras and superalgebras to integrable systems (17B80) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Overdetermined systems of PDEs with variable coefficients (35N10)

Related Items (3)

Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. II ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ New completely integrable dispersionless dynamical system of heavenly type generated by vector fields on a torus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hierarchies of Manakov-Santini type by means of Rota-Baxter and other identities
• Recursion operators and tri-Hamiltonian structure of the first heavenly equation of Plebański
• A two-component generalization of the integrable rdDym equation
• Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• On the integrability of symplectic Monge-Ampère equations
• Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras
• Classical \(R\)-matrices on Poisson algebras and related dispersionless systems
• Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables
• The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure
• Looped cotangent Virasoro algebra and nonlinear integrable systems in dimension \(2+1\)
• Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle
• Model equation of the theory of solitons
• Dispersionless integrable systems in 3D and Einstein-Weyl geometry
• Hydrodynamic reductions and solutions of a universal hierarchy
• Bi-Hamiltonian Representation, Symmetries and Integrals of Mixed Heavenly and Husain Systems
• On the Whitham hierarchy: dressing scheme, string equations and additional symmetries
• Bi-Hamiltonian nature of the equation utx = uxyuy – uyyux
• On the solutions of the second heavenly and Pavlov equations
• Anti-self-dual four–manifolds with a parallel real spinor
• On a class of integrable systems of Monge-Ampère type
• Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
• Einstein-Weyl geometry, the dKP equation and twistor theory

This page was built for publication: Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics