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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3AN0000215" target="_blank" >RIV/47813059:19610/16:N0000215 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.emis.de/journals/SIGMA/2016/032/" target="_blank" >http://www.emis.de/journals/SIGMA/2016/032/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3842/SIGMA.2016.032" target="_blank" >10.3842/SIGMA.2016.032</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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-Ampere 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-Ampere 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-Ampere equations, herewith called of Goursat type.

Název v anglickém jazyce

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

Popis výsledku anglicky

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-Ampere 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-Ampere 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-Ampere equations, herewith called of Goursat type.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

ISSN

1815-0659

e-ISSN

—

Svazek periodika

12

Číslo periodika v rámci svazku

March 2016

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

35

Strana od-do

1-35

Kód UT WoS článku

000374457100001

EID výsledku v databázi Scopus

2-s2.0-84962040811