Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics
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| Creator |
Manno, G.
Moreno, G. |
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| Description |
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.
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| Date |
2019-02-15T18:51:11Z
2019-02-15T18:51:11Z 2016 |
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| Type |
Article
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| Identifier |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics / G. Manno, G. Moreno // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53D10; 35A30; 58A30; 14M15 DOI:10.3842/SIGMA.2016.032 http://dspace.nbuv.gov.ua/handle/123456789/147730 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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