An Analysis of the Symmetries and Conservation Laws of the Class of Zakharov-Kuznetsov Equations

A. H. Kara

doi:10.3390/mca15040658

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Article

1 December 2010

An Analysis of the Symmetries and Conservation Laws of the Class of Zakharov-Kuznetsov Equations

School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

Math. Comput. Appl.2010, 15(4), 658-664;https://doi.org/10.3390/mca15040658

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Abstract

In this paper, we study and classify the conservation laws of the Zakharov- Kuznetsov equations. It is shown that these can be obtained by studying the interplay between symmetry generators and ‘multipliers’. This is, particularly, useful for the higher-order multipliers. As a final note, we include Drinfeld-Sokolov-Wilson system to demonstrate the usefulness of the approach to systems of pdes.

Keywords:

Conservation laws; symmetry generators

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