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Description
  • Jedním z výsledků teorie variačních posloupností týkajících se inverzního variačního problému je teorém, že dynamická forma $\varepsilon$, reprezentující systém parciálních diferenciálních rovnic je lokálně variační tehdy a jen tehdy, když její Helmholtzova forma $H(\varepsilon)$ je nulová. V článku je studován vztah mezi Lieovými derivacemi forem $\varepsilon$ a $H(\varepsilon)$. Je ukázáno, že invariance Helmholtzovy formy $H(\varepsilon)$ vzhledem k vektorovému poli $Z$, které zachovává kontaktní formy, je ekvivalentní s lokální variačností Lieovy derivace formy $\varepsilon$ vzhledem k poli $Z$. (cs)
  • One of the results of the variational sequence theory, related to the inverse problem of the calculus of variations, states that a dynamical form $\varepsilon$, representing a system of partial differential equations, is locally variational if and only if the Helmholtz form $H(\varepsilon)$ vanishes. In this paper, a relationship between the Lie derivatives of $\varepsilon$ and $H(\varepsilon)$ is studied. It is shown that invariance of the Helmholtz form $H(\varepsilon)$ with respect to a vector field $Z$ preserving contact forms is equivalent with local variationality of the Lie derivative of $\varepsilon$ by $Z$.
  • One of the results of the variational sequence theory, related to the inverse problem of the calculus of variations, states that a dynamical form $\varepsilon$, representing a system of partial differential equations, is locally variational if and only if the Helmholtz form $H(\varepsilon)$ vanishes. In this paper, a relationship between the Lie derivatives of $\varepsilon$ and $H(\varepsilon)$ is studied. It is shown that invariance of the Helmholtz form $H(\varepsilon)$ with respect to a vector field $Z$ preserving contact forms is equivalent with local variationality of the Lie derivative of $\varepsilon$ by $Z$. (en)
Title
  • Contact symmetries and variational sequences
  • Contact symmetries and variational sequences (en)
  • Kontaktní symetrie a variační posloupnosti (cs)
skos:prefLabel
  • Contact symmetries and variational sequences
  • Contact symmetries and variational sequences (en)
  • Kontaktní symetrie a variační posloupnosti (cs)
skos:notation
  • RIV/61989592:15310/05:00001833!RIV06-MSM-15310___
http://linked.open.../vavai/riv/strany
  • 599-609
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/03/0512), Z(MSM 153100011), Z(MSM6198959214)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 516254
http://linked.open...ai/riv/idVysledku
  • RIV/61989592:15310/05:00001833
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Fibered manifold; Lagrangian; variational sequence; contact form; contact symmetry; Helmholtz form (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [C30F23B2BBB1]
http://linked.open...v/mistoKonaniAkce
  • Praha
http://linked.open...i/riv/mistoVydani
  • Praha
http://linked.open...i/riv/nazevZdroje
  • Differential Geometry and its Applications
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Krupková, Olga
  • Krupka, Demeter
  • Prince, G.
  • Sarlet, W.
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
http://purl.org/ne...btex#hasPublisher
  • Univerzita Karlova v Praze
https://schema.org/isbn
  • 80-86732-63-0
http://localhost/t...ganizacniJednotka
  • 15310
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