# The moving frames for differential equations. II. Underdetermined and functional equations

Archivum Mathematicum (2004)

- Volume: 040, Issue: 1, page 69-88
- ISSN: 0044-8753

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topTryhuk, Václav, and Dlouhý, Oldřich. "The moving frames for differential equations. II. Underdetermined and functional equations." Archivum Mathematicum 040.1 (2004): 69-88. <http://eudml.org/doc/249319>.

@article{Tryhuk2004,

abstract = {Continuing the idea of Part I, we deal with more involved pseudogroup of transformations $\bar\{x\}=\varphi (x)$, $\bar\{y\}=L(x)y$, $\bar\{z\}=M(x)z,\, \ldots $ applied to the first order differential equations including the underdetermined case (i.e. the Monge equation $y^\{\prime \}=f(x,y,z,z^\{\prime \})$) and certain differential equations with deviation (if $z=y(\xi (x))$ is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the method of moving frames adapted to the theory of differential and functional-differential equations.},

author = {Tryhuk, Václav, Dlouhý, Oldřich},

journal = {Archivum Mathematicum},

keywords = {pseudogroup; moving frame; equivalence of differential equations; differential equations with delay; pseudogroup; equivalence of differential equations; differential equations with delay},

language = {eng},

number = {1},

pages = {69-88},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {The moving frames for differential equations. II. Underdetermined and functional equations},

url = {http://eudml.org/doc/249319},

volume = {040},

year = {2004},

}

TY - JOUR

AU - Tryhuk, Václav

AU - Dlouhý, Oldřich

TI - The moving frames for differential equations. II. Underdetermined and functional equations

JO - Archivum Mathematicum

PY - 2004

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 040

IS - 1

SP - 69

EP - 88

AB - Continuing the idea of Part I, we deal with more involved pseudogroup of transformations $\bar{x}=\varphi (x)$, $\bar{y}=L(x)y$, $\bar{z}=M(x)z,\, \ldots $ applied to the first order differential equations including the underdetermined case (i.e. the Monge equation $y^{\prime }=f(x,y,z,z^{\prime })$) and certain differential equations with deviation (if $z=y(\xi (x))$ is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the method of moving frames adapted to the theory of differential and functional-differential equations.

LA - eng

KW - pseudogroup; moving frame; equivalence of differential equations; differential equations with delay; pseudogroup; equivalence of differential equations; differential equations with delay

UR - http://eudml.org/doc/249319

ER -

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