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Symmetry-invariant conservation laws of partial differential equations†

Published online by Cambridge University Press:  13 March 2017

STEPHEN C. ANCO  and
ABDUL H. KARA
STEPHEN C. ANCO
Affiliation:
Department of Mathematics and Statistics, Brock University St. Catharines, ON L2S3A1, Canada email: sanco@brocku.ca
ABDUL H. KARA
Affiliation:
School of Mathematics, University of the Witwatersrand Wits 2050, Johannesburg, South Africa email: abdul.kara@wits.ac.za
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Abstract

A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are applied to several examples of physically interest, including the generalized Korteveg-de Vries equation, a non-Newtonian generalization of Burger's equation, the b-family of peakon equations, and the Navier–Stokes equations for compressible, viscous fluids in two dimensions.

Keywords

conservation lawsymmetrysymmetry-invariantsymmetry-homogeneousmultipliers
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 1 , February 2018 , pp. 78 - 117
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

†

S.C. Anco is supported by an NSERC research grant.

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