Lie Symmetry Analysis of the Hopf Functional-Differential Equation
نویسندگان
چکیده
منابع مشابه
Lie Symmetry Analysis of the Hopf Functional-Differential Equation
In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extend...
متن کاملComments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536-1566
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 ...
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Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to il...
متن کاملReply to Frewer et al. Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536-1566
Marta Wacławczyk 1,*, Daniel D. Janocha 2,† and Martin Oberlack 2,† 1 Institute of Geophysics, Faculty of Physics, University of Warsaw, Pasteura 7, 02-093 Warsaw, Poland 2 Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany; [email protected] (D.D.J.); [email protected] (M.O.) * Correspondence: marta.waclawczyk...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2015
ISSN: 2073-8994
DOI: 10.3390/sym7031536