On the integrability of symplectic Monge–Ampère equations

@article{Doubrov2010OnTI,
  title={On the integrability of symplectic Monge–Amp{\`e}re equations},
  author={B. Doubrov and E. Ferapontov},
  journal={Journal of Geometry and Physics},
  year={2010},
  volume={60},
  pages={1604-1616}
}
Abstract Let u be a function of n independent variables x 1 , … , x n , and let U = ( u i j ) be the Hessian matrix of u . The symplectic Monge–Ampere equation is defined as a linear relation among all possible minors of U . Particular examples include the equation det U = 1 governing improper affine spheres and the so-called heavenly equation, u 13 u 24 − u 23 u 14 = 1 , describing self-dual Ricci-flat 4 -manifolds. In this paper we classify integrable symplectic Monge–Ampere equations in four… Expand
Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property
The integrable heavenly type equations and their Lie-algebraic structure
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