Meta-Symplectic Geometry of $3^{\rm rd}$ Order Monge-Amp\`ere Equations and their Characteristics
Abstract
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-Amp\`ere equations, by using the so-called "meta-symplectic structure" associated with the 8D prolongation of a 5D contact manifold . We write down a geometric definition of a third-order Monge-Amp\`ere equation in terms of a (class of) differential two-form on . 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-Amp\`ere equations, herewith called of Goursat type.
Keywords
Cite
@article{arxiv.1403.3521,
title = {Meta-Symplectic Geometry of $3^{\rm rd}$ Order Monge-Amp\`ere Equations and their Characteristics},
author = {Gianni Manno and Giovanni Moreno},
journal= {arXiv preprint arXiv:1403.3521},
year = {2016}
}