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Symmetries and conservation laws.
Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
(Engelska)Manuskript (Övrigt vetenskapligt)
Nationell ämneskategori
Fysik
Forskningsämne
Naturvetenskap, Fysik
Identifikatorer
URN: urn:nbn:se:vxu:diva-4840OAI: oai:DiVA.org:vxu-4840DiVA, id: diva2:206539
Anmärkning

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

Tillgänglig från: 2009-02-27 Skapad: 2009-02-27 Senast uppdaterad: 2014-09-25Bibliografiskt granskad
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1. Symmetries and conservation laws
Öppna denna publikation i ny flik eller fönster >>Symmetries and conservation laws
2009 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Växjö: Växjö University Press, 2009. s. 90
Serie
Acta Wexionensia, ISSN 1404-4307 ; 170/2009
Nyckelord
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
Nationell ämneskategori
Annan fysik
Identifikatorer
urn:nbn:se:vxu:diva-2587 (URN)978-91-7636-650-9 (ISBN)
Disputation
2009-03-03, Weber, Växjö universitet, 351 95, Växjö, 13:00
Opponent
Handledare
Tillgänglig från: 2009-02-27 Skapad: 2009-02-27 Senast uppdaterad: 2010-03-10Bibliografiskt granskad

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