# Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics

created by moreno on 20 May 2016

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Published Paper

Inserted: 20 may 2016
Last Updated: 20 may 2016

Journal: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume: 12
Number: 032
Pages: 35 pages
Year: 2016
Doi: http://dx.doi.org/10.3842/SIGMA.2016.032
This paper is a natural companion of Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177, generalising its perspectives and results to the context of third-order (2D) Monge-Ampère equations, by using the so-called ''meta-symplectic structure'' associated with the 8D prolongation $M^{(1)}$ of a 5D contact manifold $M$. We write down a geometric definition of a third-order Monge-Ampère equation in terms of a (class of) differential two-form on $M^{(1)}$. In particular, the equations corresponding to decomposable forms admit a simple description in terms of certain three-dimensional distributions, which are made from the characteristics of the original equations. We conclude the paper with a study of the intermediate integrals of these special Monge-Ampère equations, herewith called of Goursat type.