Publication detail

Equivalence and symmetries of first order differential equations

TRYHUK, V.

Original Title

Equivalence and symmetries of first order differential equations

Type

journal article - other

Language

English

Original Abstract

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 of auxiliary functional equations.

Keywords

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

Authors

TRYHUK, V.

RIV year

2008

Released

1. 10. 2008

Publisher

ČSAV

Location

Praha

ISBN

0011-4642

Periodical

Czechoslovak Mathematical Journal

Year of study

58

Number

133

State

Czech Republic

Pages from

605

Pages to

635

Pages count

31

BibTex

@article{BUT45110,
  author="Václav {Tryhuk}",
  title="Equivalence and symmetries of first order differential equations",
  journal="Czechoslovak Mathematical Journal",
  year="2008",
  volume="58",
  number="133",
  pages="605--635",
  issn="0011-4642"
}