Helmholtz conditions and their generalizations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F10%3AA13016BX" target="_blank" >RIV/61988987:17310/10:A13016BX - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Helmholtz conditions and their generalizations

Popis výsledku v původním jazyce

The Euler-Lagrange morphism E1 is well-understood. It is also known that the kernel of the Helmholtz morphism E2 consists of locally variational dynamical forms, and is characterized by Helmholtz conditions. We study the image of E2 and the kernel of thenext morphism E3, and solve the corresponding local and global inverse problem when a three-form comes from a dynamical form, i.e., corresponds to a system of diferential equations. We find identities, that are a generalization of the Helmholtz conditions to this situation, and show that the problem is closely related to the question on existence of a closed three-form. The obtained results extend known results on Lagrangians and locally variational dynamical forms to general dynamical forms, and opena new possibility to study non-variational equations by means of closed three-forms, as a parallel to extremal problems (variational equations) that are studied by means of closed two-forms (Cartan forms, symplectic geometry).

Název v anglickém jazyce

Helmholtz conditions and their generalizations

Popis výsledku anglicky

The Euler-Lagrange morphism E1 is well-understood. It is also known that the kernel of the Helmholtz morphism E2 consists of locally variational dynamical forms, and is characterized by Helmholtz conditions. We study the image of E2 and the kernel of thenext morphism E3, and solve the corresponding local and global inverse problem when a three-form comes from a dynamical form, i.e., corresponds to a system of diferential equations. We find identities, that are a generalization of the Helmholtz conditions to this situation, and show that the problem is closely related to the question on existence of a closed three-form. The obtained results extend known results on Lagrangians and locally variational dynamical forms to general dynamical forms, and opena new possibility to study non-variational equations by means of closed three-forms, as a parallel to extremal problems (variational equations) that are studied by means of closed two-forms (Cartan forms, symplectic geometry).

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2010

Kód důvěrnosti údajů

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

Název periodika

Balkan Journal of Geometry and Its Applications

ISSN

1224-2780

e-ISSN

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Svazek periodika

15

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

RO - Rumunsko

Počet stran výsledku

10

Strana od-do

80-89

Kód UT WoS článku

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EID výsledku v databázi Scopus

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