Detail publikačního výsledku

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

CHRASTINOVÁ, V.; TRYHUK, V.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

CHRASTINOVÁ, V.; TRYHUK, V.

Rok RIV

2017

Vydáno

04.11.2016

Nakladatel

De Gruyter

Místo

Bratislava

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Svazek

66

Číslo

4

Stát

Slovenská republika

Strany od

999

Strany do

1018

Strany počet

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"
}