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Construction of Conservation Laws Using Symmetries
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
2014 (English)Conference paper, (Refereed)
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.

Place, publisher, year, edition, pages
Berlin: SPRINGER-VERLAG , 2014.
Keyword [en]
NONLINEAR HEAT-CONDUCTION, SHORT-PULSE EQUATION, COMPTON-SCATTERING, WAVE EQUATION, PHOTON GAS, DIFFUSION, SPECTRUM, TRANSFORMATION, ELECTRONS, SYSTEMS
National Category
Mathematical Analysis Applied Mechanics
Identifiers
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 (print)OAI: oai:DiVA.org:bth-6399DiVA: diva2:833903
Conference
EUROMECH Workshop on Similarity, Symmetry and Group Theoretical Methods in Mechanics , Varna, BULGARIA, JUN 06-09, 2013
Note

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

Available from: 2015-03-06 Created: 2015-03-06 Last updated: 2016-01-29Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
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  • ieee
  • modern-language-association-8th-edition
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More styles
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