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Construction of Conservation Laws Using Symmetries
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för matematik och naturvetenskap.
2014 (engelsk)Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

The concept of nonlinear self-adjointness of differential equations, introduced by the author in 2010, is discussed in detail. All linear equations and systems are nonlinearly self-adjoint. Moreover, the class of nonlinearly self-adjoint equations includes all nonlinear equations and systems having at least one local conservation law. It follows, in particular, that the integrable systems possessing infinite set of Lie-Backlund symmetries (higher-order tangent transformations) are nonlinearly self-adjoint. An explicit formula for conserved vectors associated with symmetries is provided for all nonlinearly self-adjoint differential equations and systems. The number of equations contained in the systems under consideration can be different from the number of dependent variables. A utilization of conservation laws for constructing exact solutions is discussed and illustrated by computing non-invariant solutions of the Chaplygin equations in gas dynamics.

sted, utgiver, år, opplag, sider
Berlin: SPRINGER-VERLAG , 2014.
Emneord [en]
NONLINEAR HEAT-CONDUCTION, SHORT-PULSE EQUATION, COMPTON-SCATTERING, WAVE EQUATION, PHOTON GAS, DIFFUSION, SPECTRUM, TRANSFORMATION, ELECTRONS, SYSTEMS
HSV kategori
Identifikatorer
URN: urn:nbn:se:bth-6399DOI: 10.1007/978-3-319-08296-7_2ISI: 000348424300002ISBN: 978-3-319-08296-7; 978-3-319-08295-0 (tryckt)OAI: oai:DiVA.org:bth-6399DiVA, id: diva2:833903
Konferanse
EUROMECH Workshop on Similarity, Symmetry and Group Theoretical Methods in Mechanics , Varna, BULGARIA, JUN 06-09, 2013
Merknad

Pulished in SIMILARITY AND SYMMETRY METHODS: APPLICATIONS IN ELASTICITY AND MECHANICS OF MATERIALS Book Series: Lecture Notes in Applied and Computational Mechanics

Tilgjengelig fra: 2015-03-06 Laget: 2015-03-06 Sist oppdatert: 2016-01-29bibliografisk kontrollert

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