The Lagrangian Order-Reduction Theorem in Field Theories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901Z2S" target="_blank" >RIV/61988987:17310/18:A1901Z2S - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00220-018-3129-5" target="_blank" >http://dx.doi.org/10.1007/s00220-018-3129-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00220-018-3129-5" target="_blank" >10.1007/s00220-018-3129-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Lagrangian Order-Reduction Theorem in Field Theories

Popis výsledku v původním jazyce

It is known that for every system of variational second order PDEs affine in second derivatives the Tonti Lagrangian is locally reducible to an equivalent first order Lagrangian (Order reduction Theorem). In this paper, a new proof is presented, based on investigation of closed forms related with variational equations, and an explicit formula for the first order Lagrangians arising by order reduction is found. The presented approach extends and completes the Order reduction Theorem by a geometric content and physical meaning of order reducibility: all variational second order PDEs affine in second derivatives admit a first-order covariant Hamiltonian formulation (Hamilton-De Donder equations), i.e. (under certain regularity conditions) carry a multisymplectic structure which is determined directly from the Euler-Lagrange expressions

Název v anglickém jazyce

The Lagrangian Order-Reduction Theorem in Field Theories

Popis výsledku anglicky

It is known that for every system of variational second order PDEs affine in second derivatives the Tonti Lagrangian is locally reducible to an equivalent first order Lagrangian (Order reduction Theorem). In this paper, a new proof is presented, based on investigation of closed forms related with variational equations, and an explicit formula for the first order Lagrangians arising by order reduction is found. The presented approach extends and completes the Order reduction Theorem by a geometric content and physical meaning of order reducibility: all variational second order PDEs affine in second derivatives admit a first-order covariant Hamiltonian formulation (Hamilton-De Donder equations), i.e. (under certain regularity conditions) carry a multisymplectic structure which is determined directly from the Euler-Lagrange expressions

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

COMMUN MATH PHYS

ISSN

0010-3616

e-ISSN

1432-0916

Svazek periodika

362

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

107-128

Kód UT WoS článku

000440111100003

EID výsledku v databázi Scopus

2-s2.0-85044950046