| Title:
|
Equivalence and symmetries of first order differential equations (English) |
| Author:
|
Tryhuk, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
605-635 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
differential equations with deviations |
| Keyword:
|
equivalence of differential equations |
| Keyword:
|
symmetry of differential equation |
| Keyword:
|
differential invariants |
| Keyword:
|
moving frames |
| MSC:
|
34A30 |
| MSC:
|
34A34 |
| MSC:
|
34K05 |
| MSC:
|
34K17 |
| idZBL:
|
Zbl 1174.34051 |
| idMR:
|
MR2455926 |
| . |
| Date available:
|
2010-07-20T13:55:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140409 |
| . |
| Reference:
|
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