Publication detail

Equivalence and symmetries of second--order differential equations

TRYHUK, V. DLOUHÝ, O.

Original Title

Equivalence and symmetries of second--order differential equations

Type

journal article - other

Language

English

Original Abstract

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.

Keywords

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

Authors

TRYHUK, V.; DLOUHÝ, O.

RIV year

2008

Released

1. 10. 2008

Publisher

SAV

Location

Bratislava

ISBN

0139-9918

Periodical

Mathematica Slovaca

Year of study

58

Number

5

State

Slovak Republic

Pages from

541

Pages to

566

Pages count

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"
}