# Equivalence and symmetries of first order differential equations

Czechoslovak Mathematical Journal (2008)

- Volume: 58, Issue: 3, page 605-635
- ISSN: 0011-4642

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topTryhuk, V.. "Equivalence and symmetries of first order differential equations." Czechoslovak Mathematical Journal 58.3 (2008): 605-635. <http://eudml.org/doc/37856>.

@article{Tryhuk2008,

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, 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.},

author = {Tryhuk, V.},

journal = {Czechoslovak Mathematical Journal},

keywords = {differential equations with deviations; equivalence of differential equations; symmetry of differential equation; differential invariants; moving frames; differential equations with deviations; equivalence of differential equations; symmetry of differential equation; differential invariants; moving frames},

language = {eng},

number = {3},

pages = {605-635},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Equivalence and symmetries of first order differential equations},

url = {http://eudml.org/doc/37856},

volume = {58},

year = {2008},

}

TY - JOUR

AU - Tryhuk, V.

TI - Equivalence and symmetries of first order differential equations

JO - Czechoslovak Mathematical Journal

PY - 2008

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 58

IS - 3

SP - 605

EP - 635

AB - 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.

LA - eng

KW - differential equations with deviations; equivalence of differential equations; symmetry of differential equation; differential invariants; moving frames; differential equations with deviations; equivalence of differential equations; symmetry of differential equation; differential invariants; moving frames

UR - http://eudml.org/doc/37856

ER -

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