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Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för matematik och naturvetenskap.
2013 (Engelska)Ingår i: Russian Mathematical Surveys, ISSN 0036-0279, E-ISSN 1468-4829, Vol. 68, nr 5, s. 889-921Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions.

Ort, förlag, år, upplaga, sidor
TURPION LTD, IOP PUBLISHING , 2013. Vol. 68, nr 5, s. 889-921
Nyckelord [en]
differential equations, nonlinear self-adjointness, conservation laws, exact solutions
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:bth-6762DOI: 10.1070/RM2013v068n05ABEH004860ISI: 000329123400003Lokalt ID: oai:bth.se:forskinfo3FF20C187CC2A1A3C1257C980034DD66OAI: oai:DiVA.org:bth-6762DiVA, id: diva2:834303
Tillgänglig från: 2014-03-11 Skapad: 2014-03-11 Senast uppdaterad: 2017-12-04Bibliografiskt granskad

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