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Comment on 'Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives'

Willy Sarlet (UGent)
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Abstract
In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error.

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Citation

Please use this url to cite or link to this publication:

Chicago
Sarlet, Willy. 2010. “Comment on ‘Conservation Laws of Higher Order Nonlinear PDEs and the Variational Conservation Laws in the Class with Mixed Derivatives’.” Journal of Physics A-mathematical and Theoretical.
APA
Sarlet, Willy. (2010). Comment on “Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL.
Vancouver
1.
Sarlet W. Comment on “Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives.”JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2010.
MLA
Sarlet, Willy. “Comment on ‘Conservation Laws of Higher Order Nonlinear PDEs and the Variational Conservation Laws in the Class with Mixed Derivatives’.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2010 : n. pag. Print.
@misc{1088364,
  abstract     = {In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error.},
  articleno    = {458001},
  author       = {Sarlet, Willy},
  issn         = {1751-8113},
  language     = {eng},
  number       = {45},
  pages        = {6},
  series       = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  title        = {Comment on 'Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives'},
  url          = {http://dx.doi.org/10.1088/1751-8113/43/45/458001},
  volume       = {43},
  year         = {2010},
}

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