## 62 Citations

### The moment map on the space of symplectic 3D Monge-Amp\`ere equations

- Mathematics
- 2021

For any 2nd order scalar PDE E in one unknown function, that we interpret as a hypersurface of a 2nd order jet space J2, we construct, by means of the characteristics of E, a sub–bundle of the…

### Integrability of Dispersionless Hirota-Type Equations and the Symplectic Monge–Ampère Property

- MathematicsInternational Mathematics Research Notices
- 2020

We prove that integrability of a dispersionless Hirota-type equation implies the symplectic Monge–Ampère property in any dimension $\geq 4$. In 4D, this yields a complete classification of…

### A Geometry for Second-Order PDEs and their Integrability, Part I

- Mathematics
- 2010

For the purpose of understanding second-order scalar PDEs and their hydrodynamic integrability, we introduce G-structures that are induced on hypersurfaces of the space of symmetric matrices…

### Lie-algebraic structure of Lax–Sato integrable heavenly equations and the Lagrange–d’Alembert principle

- Mathematics
- 2017

### Contact geometry of multidimensional Monge-Ampere equations: characteristics, intermediate integrals and solutions

- Mathematics
- 2010

We study the geometry of multidimensional scalar 2 order PDEs (i.e. PDEs with n independent variables) with one unknown function, viewed as hypersurfaces E in the Lagrangian Grassmann bundle M (1)…

### Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations

- MathematicsJournal of Geometry and Physics
- 2019

### The integrable heavenly type equations and their Lie-algebraic structure

- Physics
- 2016

There are investigated the Lie algebraic structure and integrability properties of a very interesting class of nonlinear dynamical systems called the heavenly equations, which were initiated by…

### Conformal geometry of surfaces in the Lagrangian Grassmannian and second‐order PDE

- Mathematics
- 2012

Of all real Lagrangian Grassmannians LG(n, 2n), only LG(2, 4) admits a distinguished Lorentzian conformal structure and hence is identified with the indefinite Möbius space S1,2. Using Cartan's…

### Generalization of bi-Hamiltonian systems in (3+1) dimension, possessing partner symmetries

- Mathematics
- 2016

### On integrability in Grassmann geometries: integrable systems associated with fourfolds in Gr(3,5)

- Mathematics
- 2015

Let Gr(d,n) be the Grassmannian of d ‐dimensional linear subspaces of an n ‐dimensional vector space Vn . A submanifold X⊂Gr(d,n) gives rise to a differential system Σ(X) that governs d ‐dimensional…

## References

SHOWING 1-10 OF 48 REFERENCES

### A classification of Monge-Ampère equations

- Mathematics
- 1993

A classical problem of a local classification of non-linear equation arising in S. Lie works is studied for the most natural class of Monge-Ampere equations (M.A.E.) on a smooth manifold M". We solve…

### Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian

- Mathematics
- 2007

We investigate integrable second-order equations of the formwhich typically arise as the Hirota-type relations for various (2 + 1)-dimensional dispersionless hierarchies. Familiar examples include…

### Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability

- Mathematics
- 2004

A (d+1)-dimensional dispersionless PDE is said to be integrable if its n-component hydrodynamic reductions are locally parametrized by (d−1)n arbitrary functions of one variable. The most important…

### Hyper-Kähler Hierarchies and Their Twistor Theory

- Mathematics
- 2000

Abstract: A twistor construction of the hierarchy associated with the hyper-Kähler equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given. The…

### Contact geometry and non-linear differential equations

- Mathematics
- 2007

Introduction Part I. Symmetries and Integrals: 1. Distributions 2. Ordinary differential equations 3. Model differential equations and Lie superposition principle Part II. Symplectic Algebra: 4.…

### On the solutions of the second heavenly and Pavlov equations

- Mathematics
- 2009

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of…

### On classification of second-order PDEs possessing partner symmetries

- Mathematics
- 2009

Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of the heavenly equations of Plebañski that govern heavenly gravitational metrics. In this paper, we…

### On self-dual gravity.

- MathematicsPhysical review. D, Particles and fields
- 1993

The Ashtekar-Jacobson-Smolin equations are studied and it is found that any self-dual metric can be characterised by a function that satisfies a nonlinear evolution equation, to which the general solution can be found iteratively.

### On the Integrability of (2+1)-Dimensional Quasilinear Systems

- Mathematics
- 2004

A (2+1)-dimensional quasilinear system is said to be ‘integrable’ if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Riemann invariants.…