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Response to “Comment on ‘Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation’” [J. Math. Phys. 57, 034102 (2016)]
1.M. Wacławczyk and M. Oberlack, “Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation,” J. Math. Phys. 54, 072901 (2013).
2.E. Hopf, “Statistical hydromechanics and functional calculus,” J. Rat. Mech. Anal. 1, 87 (1952).
3.M. Oberlack and A. M. Rosteck, “New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws,” Discrete Contin. Dyn. Syst.–Ser. S 3, 451 (2010).
4.A. M. Rosteck and M. Oberlack, “Lie algebra of the symmetries of the multi-point equations in statistical turbulence theory,” J. Nonlinear Math. Phys. 18, 251 (2011).
5.M. Wacławczyk, S. Nicola, M. Oberlack, A. Rosteck, M. Wilczek, and R. Friedrich, “Statistical symmetries of the Lundgren-Monin-Novikov hierarchy,” Phys. Rev. E 90, 013022 (2014).
6.D. Janocha, M. Wacławczyk, and M. Oberlack, “Lie symmetry analysis of the Hopf functional-differential equation,” Symmetry 7, 1536–1566 (2015).
7.M. Oberlack and M. Wacławczyk, “On the extension of Lie group analysis to functional differential equations,” Arch. Mech. 58, 597 (2006).
8.D. Janocha, “Lie symmetry analysis of the Hopf functional-differential equation,” Master thesis,TU Darmstadt, 2015.
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We address the criticism of Frewer et al. concerning the paper “Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation” [J. Math. Phys. 54, 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 et al. 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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