On the Redefinition of the Variational and `Partial' Variational Conservation Laws in a Class of Nonlinear PDEs with Mixed Derivatives

R. Narain; A. H. Kara

doi:10.3390/mca15040732

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Article

1 December 2010

On the Redefinition of the Variational and `Partial' Variational Conservation Laws in a Class of Nonlinear PDEs with Mixed Derivatives

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School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

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Math. Comput. Appl.2010, 15(4), 732-741;https://doi.org/10.3390/mca15040732

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Abstract

The construction of conserved vectors using Noether’s and partial Noether’s theorems are carried out for high order PDEs with mixed derivatives. The resultant conserved flows display some interesting ‘divergence properties’ owing to the existence of the mixed derivatives. These are spelled out for various equations from mathematical physics.

Keywords:

Noether’s theorem; mixed derivatives; conservation laws

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