Publication result detail

Report on the Absolute Differential Equations I

CHRASTINOVÁ, V.; TRYHUK, V.

Original Title

Report on the Absolute Differential Equations I

English Title

Report on the Absolute Differential Equations I

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

The article provides a survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical tools follows. In particular the external, internal, generalized and higher–order symmetries and infinitesimal symmetries together with the E. Cartan’s prolongations, various characteristics, the involutivity and the controllability structures are clarified in genuinely coordinate–free terms without any use of the common jet mechanisms.

English abstract

The article provides a survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical tools follows. In particular the external, internal, generalized and higher–order symmetries and infinitesimal symmetries together with the E. Cartan’s prolongations, various characteristics, the involutivity and the controllability structures are clarified in genuinely coordinate–free terms without any use of the common jet mechanisms.

Keywords

Higher–order transformations, symmetry, diffiety, involutivity, controllability, characteristics.

Key words in English

Higher–order transformations, symmetry, diffiety, involutivity, controllability, characteristics.

Authors

CHRASTINOVÁ, V.; TRYHUK, V.

RIV year

2018

Released

20.01.2017

Publisher

Isaac Scientific Publishing Co.

Location

Hong Kong

ISBN

2518-3680

Periodical

Advances in Analysis

Volume

2

Number

1

State

People's Republic of China

Pages from

41

Pages to

61

Pages count

21

URL

http://www.isaacpub.org/images/PaperPDF/AAN_100029_2017012014404604851.pdf

BibTex

@article{BUT133853,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="Report on the Absolute Differential Equations I",
  journal="Advances in Analysis",
  year="2017",
  volume="2",
  number="1",
  pages="41--61",
  doi="10.22606/aan.2017.11007",
  issn="2518-3680",
  url="http://www.isaacpub.org/images/PaperPDF/AAN_100029_2017012014404604851.pdf"
}