Symmetries and conservation laws
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2009 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Symmetrier och konserveringslagar (Swedish)
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. , 90 pages p.
Acta Wexionensia, ISSN 1404-4307 ; 170
Conservation law, Noether’s theorem, Lie group analysis, Lie-Bäcklund transformations, basis of conservation laws, formal Lagrangian, self-adjoint equation, quasi-self-adjoint equation, nonlocal conservation law
Mathematics Mathematical Analysis
IdentifiersURN: urn:nbn:se:bth-00437Local ID: oai:bth.se:forskinfoD2A098F807334F13C125758D0037C63FISBN: 978-91-7636-650-9OAI: oai:DiVA.org:bth-00437DiVA: diva2:835925
Thesis for the degree of Doctor of Philosophy2012-09-182009-04-032015-09-28Bibliographically approved