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Symmetries and conservation laws

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.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:vxu-2587
Date January 2009
CreatorsKhamitova, Raisa
PublisherVäxjö universitet, Matematiska och systemtekniska institutionen, Växjö : Växjö University Press
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeDoctoral thesis, comprehensive summary, info:eu-repo/semantics/doctoralThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess
RelationActa Wexionensia, 1404-4307 ; 170/2009

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