Bi-Hamiltonian Representation, Symmetries and Integrals of Mixed Heavenly and Husain Systems

DOI10.1142/S1402925110001021zbMath1235.37021arXiv0904.3981WikidataQ114072110 ScholiaQ114072110MaRDI QIDQ2996754

Mikhail B. Sheftel, Devrim Yazıcı

Publication date: 3 May 2011

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

Full work available at URL: https://arxiv.org/abs/0904.3981

zbMATH Keywords

integralssymmetriesNoether theoremLax pairbi-Hamiltonian representationsymplectic two-form

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items

Recursion operators and tri-Hamiltonian structure of the first heavenly equation of Plebański, Recursion operators and bi-Hamiltonian structure of the general heavenly equation, Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I, Lax pairs, recursion operators and bi-Hamiltonian representations of \((3+1)\)-dimensional Hirota type equations, Generalization of bi-Hamiltonian systems in \((3+1)\) dimension, possessing partner symmetries, Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics, Symmetries, integrals and hierarchies of new (3+1)-dimensional bi-Hamiltonian systems of Monge-Ampère type

Cites Work

• Unnamed Item
• An analytic algorithm for decoupling and integrating systems of nonlinear partial differential equations
• A new characterization of half-flat solutions to Einstein's equation
• The Lagrangian of a self-dual gravitational field as a limit of the SDYM Lagrangian.
• Partner symmetries and non-invariant solutions of four-dimensional heavenly equations
• Evolution equations possessing infinitely many symmetries
• Partner symmetries of the complex Monge–Amp re equation yield hyper-K hler metrics without continuous symmetries
• Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics