Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536-1566

被引：1

作者：

Frewer, Michael ^{[1
]}

Khujadze, George ^{[2
]}

机构：

[1] Trubnerstr 42, D-69121 Heidelberg, Germany

[2] Univ Siegen, Chair Fluid Mech, D-57068 Siegen, Germany

来源：

SYMMETRY-BASEL | 2016年 / 8卷 / 04期

关键词：

Lie groups; Lie symmetries; Hopf equation; Burgers equation; functional-differential equations; symmetry breaking; turbulence;

D O I：

10.3390/sym8040023

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf-Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf-Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two of them should be replaced by their correct intermediate formulations, but which ultimately violate internal consistency constraints of the governing equation. It is concluded that the recently proposed symmetry analysis method for functional integro-differential equations should not be adopted when aiming at a consistent and complete approach.

引用

页数：26