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

Václav Tryhuk; Oldřich Dlouhý

Archivum Mathematicum (2004)

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

Abstract

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Continuing the idea of Part I, we deal with more involved pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ = L ( x ) y , z ¯ = M ( x ) z , ... applied to the first order differential equations including the underdetermined case (i.e. the Monge equation y ' = f ( x , y , z , z ' ) ) and certain differential equations with deviation (if z = y ( ξ ( 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.

How to cite

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Tryhuk, 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 -

References

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