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/content/aip/journal/jmp/57/3/10.1063/1.4944424
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/content/aip/journal/jmp/57/3/10.1063/1.4944424
2016-03-22
2016-12-07

Abstract

We address the criticism of Frewer concerning the paper “Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation” [J. Math. Phys. , 072901 (2013)]. Most importantly, we stress that we never claimed that any new statistical symmetries were found in this paper. The aim of this paper was to apply the Lie group analysis to an equation with functional derivatives and derive invariant solutions for this equation. These results still stand as they are, most important, mathematically correct. We address also other critical statements of Frewer and show that there is a connection between the translational invariance of statistics and transformations of the functional Φ. To sum up, key ideas and fundamental result in the work of Wacławczyk and Oberlack are still unaffected.

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