Publication result detail

On the internal approach to differential equations 3. Infinitesimal symmetries

CHRASTINOVÁ, V.; TRYHUK, V.

Original Title

On the internal approach to differential equations 3. Infinitesimal symmetries

English Title

On the internal approach to differential equations 3. Infinitesimal symmetries

Type

WoS Article

Original Abstract

The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order of derivatives can be changed and the article is devoted to the higher--order infinitesimal symmetries which provide a~simplifying "linear aproximation" of general groups of higher--order symmetries. The classical Lie's approach is appropriately adapted.

English abstract

The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order of derivatives can be changed and the article is devoted to the higher--order infinitesimal symmetries which provide a~simplifying "linear aproximation" of general groups of higher--order symmetries. The classical Lie's approach is appropriately adapted.

Keywords

higher--order transformations, variation, infinitesimal symmetry, diffiety, standard basis

Key words in English

higher--order transformations, variation, infinitesimal symmetry, diffiety, standard basis

Authors

CHRASTINOVÁ, V.; TRYHUK, V.

RIV year

2018

Released

27.10.2016

Publisher

Mathematical institute, Slovak Academy of Sciences, DE GRUYTER Mathematica Slovaca

Location

Bratislava

ISBN

0139-9918

Periodical

Mathematica Slovaca

Volume

66

Number

6

State

Slovak Republic

Pages from

1459

Pages to

1474

Pages count

16

URL

https://www.degruyter.com/view/j/ms.2016.66.issue-6/ms-2016-0236/ms-2016-0236.xml?rskey=3gCmsj&result=1

BibTex

@article{BUT133573,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="On the internal approach to differential equations 3. Infinitesimal symmetries",
  journal="Mathematica Slovaca",
  year="2016",
  volume="66",
  number="6",
  pages="1459--1474",
  doi="10.1515/ms-2016-0236",
  issn="0139-9918",
  url="https://www.degruyter.com/view/j/ms.2016.66.issue-6/ms-2016-0236/ms-2016-0236.xml?rskey=3gCmsj&result=1"
}