Ekvivalence a symetrie diferenciálních rovnic prvního řádu

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F08%3APU70523" target="_blank" >RIV/00216305:26110/08:PU70523 - 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

Equivalence and symmetries of first order differential equations

Popis výsledku v původním jazyce

In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations $bar x=varphi (x),$ $bar y=bar y(bar x)=L(x)y(x).$ That means, the transformed unknown function $bar y$ is obtained by means of the change of the independent variable and subsequent multiplication by a~nonvanishing factor. Instead of the common direct calculations, we use some more advanced tools from differential geometry, however, exposition is self--contained and only the most fundamental properties of differential forms are employed. We refer to analogous achievements in the literature. In particular, the generalized higher symmetry problem involving a~finite number of invariants of the kind $F^j=a_j y, Pi |z_i|^{k^j_i}=a_j y |z_1|^{k^j_1} ldots |z_m|^{k^j_m}=a_j(x)y|y(xi_1)|^{k^j_1}ldots |y(xi_m)|^{k^j_m}$ is compared to similar results obtained by means

Název v anglickém jazyce

Equivalence and symmetries of first order differential equations

Popis výsledku anglicky

In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations $bar x=varphi (x),$ $bar y=bar y(bar x)=L(x)y(x).$ That means, the transformed unknown function $bar y$ is obtained by means of the change of the independent variable and subsequent multiplication by a~nonvanishing factor. Instead of the common direct calculations, we use some more advanced tools from differential geometry, however, exposition is self--contained and only the most fundamental properties of differential forms are employed. We refer to analogous achievements in the literature. In particular, the generalized higher symmetry problem involving a~finite number of invariants of the kind $F^j=a_j y, Pi |z_i|^{k^j_i}=a_j y |z_1|^{k^j_1} ldots |z_m|^{k^j_m}=a_j(x)y|y(xi_1)|^{k^j_1}ldots |y(xi_m)|^{k^j_m}$ is compared to similar results obtained by means

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

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

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

Název periodika

Czechoslovak Mathematical Journal

ISSN

0011-4642

e-ISSN

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Svazek periodika

58

Číslo periodika v rámci svazku

133

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

31

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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