Potential  Symmetry Generators of  Some Perturbed Nonlinear Evolution Related Equations

A. H. Kara

doi:10.3390/mca8010089

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Article

1 April 2003

Potential Symmetry Generators of Some Perturbed Nonlinear Evolution Related Equations

School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, P. O. Wits 2050, Johannesburg, South Africa

Math. Comput. Appl.2003, 8(1), 89-94;https://doi.org/10.3390/mca8010089

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Abstract

Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to nonlinear systems perturbed to some order by a small parameter. The potential (or auxiliary) form of the perturbed . system necessarily requires knowledge of an "approximate" conservation law of the system. We make an analysis on a perturbed Burgers equation and discuss other nonlinear equations where the results are applicable.

Keywords:

potential; approximate symmetries

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