Equivalence and symmetries of first order differential equations

Title:

Equivalence and symmetries of first order differential equations

Creator:

Tryhuk, Václav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:20920a4d-979f-40fa-b995-3e09c40888be
uuid:20920a4d-979f-40fa-b995-3e09c40888be

Subject:

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

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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, the exposition is self-contained and only the most fundamental properties of differential forms are employed. We refer to analogous achievements in 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

605-635

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:3

Harvested from:

CDK

Metadata only:

false