Detail publikace

Equivalence and symmetries of second--order differential equations

TRYHUK, V. DLOUHÝ, O.

Originální název

Equivalence and symmetries of second--order differential equations

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

In this article we investigate the equivalence of underdetermined differential equations and differential equations with deviations of second order with respect to the pseudogroup of transformations $\bar x=\varphi (x),$ $\bar y=\bar y(\bar x)=L(x)+y(x),$ \mbox{$\bar z=\bar z(\bar x)=M(x)+z(x).$} Our main aim is to determine such equations that admit a~large pseudogroup of symmetries. Instead the common direct calculations, we use some more advanced tools from differential geometry, however, our exposition is self--contained and only the most fundamental properties of differential forms are employed.

Klíčová slova

differential equations with deviations, equivalence of differential equations, symmetry of differential equation, differential invariants, moving frames

Autoři

TRYHUK, V.; DLOUHÝ, O.

Rok RIV

2008

Vydáno

1. 10. 2008

Nakladatel

SAV

Místo

Bratislava

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Ročník

58

Číslo

5

Stát

Slovenská republika

Strany od

541

Strany do

566

Strany počet

26

BibTex

@article{BUT45111,
  author="Václav {Tryhuk} and Oldřich {Dlouhý}",
  title="Equivalence and symmetries of second--order differential equations",
  journal="Mathematica Slovaca",
  year="2008",
  volume="58",
  number="5",
  pages="541--566",
  issn="0139-9918"
}