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Article

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

by
R. Narain
* and
A. H. Kara
*
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2010, 15(4), 732-741; https://doi.org/10.3390/mca15040732
Published: 1 December 2010
Versions Notes

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 Noether’s theorem; mixed derivatives; conservation laws

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MDPI and ACS Style

Narain, R.; Kara, A.H. On the Redefinition of the Variational and `Partial' Variational Conservation Laws in a Class of Nonlinear PDEs with Mixed Derivatives. Math. Comput. Appl. 2010, 15, 732-741. https://doi.org/10.3390/mca15040732

AMA Style

Narain R, Kara AH. On the Redefinition of the Variational and `Partial' Variational Conservation Laws in a Class of Nonlinear PDEs with Mixed Derivatives. Mathematical and Computational Applications. 2010; 15(4):732-741. https://doi.org/10.3390/mca15040732

Chicago/Turabian Style

Narain, R., and A. H. Kara. 2010. "On the Redefinition of the Variational and `Partial' Variational Conservation Laws in a Class of Nonlinear PDEs with Mixed Derivatives" Mathematical and Computational Applications 15, no. 4: 732-741. https://doi.org/10.3390/mca15040732

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