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Symmetries and conservation laws.
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
(English)Manuscript (Other academic)
National Category
Physical Sciences
Research subject
Natural Science, Physics
Identifiers
URN: urn:nbn:se:vxu:diva-4840OAI: oai:DiVA.org:vxu-4840DiVA, id: diva2:206539
Note

Part of urn:nbn:se:vxu:diva-2587

Available from: 2009-02-27 Created: 2009-02-27 Last updated: 2014-09-25Bibliographically approved
In thesis
1. Symmetries and conservation laws
Open this publication in new window or tab >>Symmetries and conservation laws
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided.

Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws.

One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.

Place, publisher, year, edition, pages
Växjö: Växjö University Press, 2009. p. 90
Series
Acta Wexionensia, ISSN 1404-4307 ; 170/2009
Keyword
conservation law, Noether's theorem, Lie group analysis, Lie-Bäcklund transformations, basis of conservation laws, formal Lagrangian, self-adjoint equation, quasi-selfadjoint, equation, nonlocal conservation law
National Category
Other Physics Topics
Identifiers
urn:nbn:se:vxu:diva-2587 (URN)978-91-7636-650-9 (ISBN)
Public defence
2009-03-03, Weber, Växjö universitet, 351 95, Växjö, 13:00
Opponent
Supervisors
Available from: 2009-02-27 Created: 2009-02-27 Last updated: 2010-03-10Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf