Connections Between Symmetries and Conservation Laws

This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find the conservation laws directly for any given system of differential equations. This metho...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2005
Автор: Bluman, G.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2005
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/209349
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Connections Between Symmetries and Conservation Laws / G. Bluman // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 25 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209349
record_format dspace
spelling Bluman, G.
2025-11-19T12:27:30Z
2005
Connections Between Symmetries and Conservation Laws / G. Bluman // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 25 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 58J70; 58J72; 70G65; 70G75; 70H03; 70H33; 70S10
https://nasplib.isofts.kiev.ua/handle/123456789/209349
https://doi.org/10.3842/SIGMA.2005.011
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find the conservation laws directly for any given system of differential equations. This method yields the multipliers for conservation laws as well as an integral formula for corresponding conserved densities. The action of a symmetry (discrete or continuous) on a conservation law yields conservation laws. Conservation laws yield non-locally related systems that, in turn, can yield nonlocal symmetries and, in addition, be useful for the application of other mathematical methods. From its admitted symmetries or multipliers for conservation laws, one can determine whether or not a given system of differential equations can be linearized by an invertible transformation.
The author thanks his collaborators for much of the work presented in this paper, especially Stephen Anco, Alexei Cheviakov, Sukeyuki Kumei, and Temuerchaolu. He also acknowledges financial support from the National Sciences and Engineering Research Council of Canada.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Connections Between Symmetries and Conservation Laws
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Connections Between Symmetries and Conservation Laws
spellingShingle Connections Between Symmetries and Conservation Laws
Bluman, G.
title_short Connections Between Symmetries and Conservation Laws
title_full Connections Between Symmetries and Conservation Laws
title_fullStr Connections Between Symmetries and Conservation Laws
title_full_unstemmed Connections Between Symmetries and Conservation Laws
title_sort connections between symmetries and conservation laws
author Bluman, G.
author_facet Bluman, G.
publishDate 2005
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find the conservation laws directly for any given system of differential equations. This method yields the multipliers for conservation laws as well as an integral formula for corresponding conserved densities. The action of a symmetry (discrete or continuous) on a conservation law yields conservation laws. Conservation laws yield non-locally related systems that, in turn, can yield nonlocal symmetries and, in addition, be useful for the application of other mathematical methods. From its admitted symmetries or multipliers for conservation laws, one can determine whether or not a given system of differential equations can be linearized by an invertible transformation.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209349
citation_txt Connections Between Symmetries and Conservation Laws / G. Bluman // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 25 назв. — англ.
work_keys_str_mv AT blumang connectionsbetweensymmetriesandconservationlaws
first_indexed 2025-12-07T17:06:17Z
last_indexed 2025-12-07T17:06:17Z
_version_ 1850886066724143104