Lie Symmetry Analysis of the Hopf Functional-Differential Equation

نویسندگان

  • Daniel D. Janocha
  • Marta Waclawczyk
  • Martin Oberlack
چکیده

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 extended Lie symmetry analysis in the physical space where we have to deal with the transformation of the integration variable in the appearing integral terms. The method is based on the transformation of the product y(x)dx appearing in the integral terms and applied to the functional formulation of the viscous Burgers equation. The extended Lie symmetry analysis furnishes all known symmetries of the viscous Burgers equation and is able to provide new symmetries associated with the Hopf formulation of the viscous Burgers equation. Hence, it can be employed as an important tool for applications in continuum mechanics.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Comments 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 ...

متن کامل

Lie symmetry analysis for Kawahara-KdV equations

We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.

متن کامل

New Solutions for Fokker-Plank Equation of‎ ‎Special Stochastic Process via Lie Point Symmetries

‎In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process‎. ‎This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process‎.

متن کامل

Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

متن کامل

Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries

‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Symmetry

دوره 7  شماره 

صفحات  -

تاریخ انتشار 2015