Publication result detail

On the internal approach to differential equations 1. The involutiveness and standard basis

CHRASTINOVÁ, V.; TRYHUK, V.

Original Title

On the internal approach to differential equations 1. The involutiveness and standard basis

English Title

On the internal approach to differential equations 1. The involutiveness and standard basis

Type

WoS Article

Original Abstract

The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are subject to arbitrary transformations of variables in the widest possible sense. In this preparatory Part 1, the involutivity and the related standard bases are investigated as a~technical tool within the framework of commutative algebra. The particular case of ordinary differential equations is briefly mentioned in order to demonstrate the strength of this approach in the study of the structure, symmetries and constrained variational integrals under the simplifying condition of one independent variable. In full generality, these topics will be investigated in subsequent Parts of this article.

English abstract

The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are subject to arbitrary transformations of variables in the widest possible sense. In this preparatory Part 1, the involutivity and the related standard bases are investigated as a~technical tool within the framework of commutative algebra. The particular case of ordinary differential equations is briefly mentioned in order to demonstrate the strength of this approach in the study of the structure, symmetries and constrained variational integrals under the simplifying condition of one independent variable. In full generality, these topics will be investigated in subsequent Parts of this article.

Keywords

higher--order symmetries; diffiety; involutivity; standard basis

Key words in English

higher--order symmetries; diffiety; involutivity; standard basis

Authors

CHRASTINOVÁ, V.; TRYHUK, V.

RIV year

2017

Released

04.11.2016

Publisher

De Gruyter

Location

Bratislava

ISBN

0139-9918

Periodical

Mathematica Slovaca

Volume

66

Number

4

State

Slovak Republic

Pages from

999

Pages to

1018

Pages count

19

BibTex

@article{BUT107088,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="On the internal approach to differential equations 1. The involutiveness and standard basis",
  journal="Mathematica Slovaca",
  year="2016",
  volume="66",
  number="4",
  pages="999--1018",
  doi="10.1515/ms-2015-0198",
  issn="0139-9918"
}