On the integrability of symplectic Monge-Ampère equations
From MaRDI portal
Publication:988911
DOI10.1016/j.geomphys.2010.05.009zbMath1195.35109arXiv0910.3407OpenAlexW2027096980MaRDI QIDQ988911
Boris M. Doubrov, Evgeny V. Ferapontov
Publication date: 19 August 2010
Published in: Journal of Geometry and Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0910.3407
Second-order nonlinear hyperbolic equations (35L70) PDEs in connection with relativity and gravitational theory (35Q75) Parabolic Monge-Ampère equations (35K96) Monge-Ampère equations (35J96)
Related Items (34)
A simple construction of recursion operators for multidimensional dispersionless integrable systems ⋮ On a class of integrable systems of Monge-Ampère type ⋮ Six-dimensional heavenly equation. Dressing scheme and the hierarchy ⋮ Integrability properties of a symmetric 4 + 4-dimensional heavenly-type equation ⋮ Recursion operators and tri-Hamiltonian structure of the first heavenly equation of Plebański ⋮ Recursion operators and bi-Hamiltonian structure of the general heavenly equation ⋮ Integrability via geometry: dispersionless differential equations in three and four dimensions ⋮ Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle ⋮ On the Einstein-Weyl and conformal self-duality equations ⋮ Dispersionless Hirota equations and the genus 3 hyperelliptic divisor ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. II ⋮ Lax representations via twisted extensions of infinite-dimensional Lie algebras: some new results ⋮ Webs, Nijenhuis operators, and heavenly PDEs ⋮ Integrable dispersionless PDEs in 4D, their symmetry pseudogroups and deformations ⋮ The moment map on the space of symplectic 3D Monge-Ampère equations ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions ⋮ Lax pairs, recursion operators and bi-Hamiltonian representations of \((3+1)\)-dimensional Hirota type equations ⋮ Evolutionary Hirota type \((2+1)\)-dimensional equations: Lax pairs, recursion operators and bi-Hamiltonian structures ⋮ Dispersionless (3+1)-dimensional integrable hierarchies ⋮ On an integrable multi-dimensionally consistent 2 n + 2 n -dimensional heavenly-type equation ⋮ Second-order PDEs in four dimensions with half-flat conformal structure ⋮ Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates ⋮ Nonlocal symmetries of Plebański’s second heavenly equation ⋮ Complex solutions of Monge-Ampère equations ⋮ Isospectral deformation of the reduced quasi-classical self-dual Yang-Mills equation ⋮ Generalization of bi-Hamiltonian systems in \((3+1)\) dimension, possessing partner symmetries ⋮ Anti-self-dual gravitational metrics determined by the modified heavenly equation ⋮ Projective aspects of the geometry of Lagrangian Grassmannians and spinor varieties ⋮ Classical M. A. Buhl problem, its Pfeiffer-Sato solutions, and the classical Lagrange-d'Alembert principle for the integrable heavenly-type nonlinear equations ⋮ 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 ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators ⋮ Recursion operators for multidimensional integrable PDEs
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the \(\overline{\delta}\)-dressing method applicable to heavenly equation
- Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
- Null Lagrangians, weak continuity, and variational problems of arbitrary order
- On symplectic classification of effective 3-forms and Monge-Ampère equations.
- Construction and classification of complex simple Lie algebras via projective geometry
- On the integrability of \((2+1)\)-dimensional quasilinear systems
- The Lagrangian of a self-dual gravitational field as a limit of the SDYM Lagrangian.
- Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
- Nahm's equations and free-boundary problems
- On classification of second-order PDEs possessing partner symmetries
- On the solutions of the second heavenly and Pavlov equations
- Self-duality in four-dimensional Riemannian geometry
- A classification of Monge-Ampère equations
- Hydrodynamic reductions of the heavenly equation
- THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
- An infinite number of hidden variables in hyper-Kähler metrics
- Twistor theory of hyper-Kähler metrics with hidden symmetries
- Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability
- The symmetry structure of the anti-self-dual Einstein hierarchy
- On the heavenly equation hierarchy and its reductions
- Multi-Hamiltonian structure of Plebanski's second heavenly equation
- Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy
- Hyper-Kähler hierarchies and their twistor theory
- The projective geometry of Freudenthal's magic square.
This page was built for publication: On the integrability of symplectic Monge-Ampère equations
