scholarly journals Lie Symmetry Analysis of Burgers Equation and the Euler Equation on a Time Scale

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 10 ◽  
Author(s):  
Mingshuo Liu ◽  
Huanhe Dong ◽  
Yong Fang ◽  
Yong Zhang
Keyword(s):  
Euler Equation ◽  
Time Scale ◽  
Flow Model ◽  
Burgers Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Discrete Equations ◽  
Group Invariant Solutions

As a powerful tool that can be used to solve both continuous and discrete equations, the Lie symmetry analysis of dynamical systems on a time scale is investigated. Applying the method to the Burgers equation and Euler equation, we get the symmetry of the equation and single parameter groups on a time scale. Some group invariant solutions in explicit form for the traffic flow model simulated by a Burgers equation and Euler equation with a Coriolis force on a time scale are studied.

scholarly journals Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

2018 ◽  
Vol 331 ◽  
pp. 457-472 ◽  
Author(s):  
K. Sakkaravarthi ◽  
A.G. Johnpillai ◽  
A. Durga Devi ◽  
T. Kanna ◽  
M. Lakshmanan
Keyword(s):  
Helmholtz Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Invariant Solutions ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Group Invariant Solutions

Group Invariant Solutions and Conservation Laws of the Fornberg– Whitham Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 489-496 ◽  
Author(s):  
Mir Sajjad Hashemi ◽  
Ali Haji-Badali ◽  
Parisa Vafadar
Keyword(s):  
Exact Solutions ◽  
Reduction Method ◽  
Lie Symmetry ◽  
First Integrals ◽  
Invariant Solutions ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Whitham Equation

In this paper, we utilize the Lie symmetry analysis method to calculate new solutions for the Fornberg-Whitham equation (FWE). Applying a reduction method introduced by M. C. Nucci, exact solutions and first integrals of reduced ordinary differential equations (ODEs) are considered. Nonlinear self-adjointness of the FWE is proved and conserved vectors are computed

scholarly journals Lie Symmetry Analysis of Kudryashov-Sinelshchikov Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Mehdi Nadjafikhah ◽  
Vahid Shirvani-Sh
Keyword(s):  
Nonlinear Evolution ◽  
Lie Symmetry ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Lie Symmetry Method ◽  
Group Invariant Solutions ◽  
Fifth Order ◽  
Symmetry Method ◽  
Preliminary Classification

The Lie symmetry method is performed for the fifth-order nonlinear evolution Kudryashov-Sinelshchikov equation. We will find ones and two-dimensional optimal systems of Lie subalgebras. Furthermore, preliminary classification of its group-invariant solutions is investigated.

scholarly journals Symmetry Reductions for a Generalized Fifth Order KdV Equation

2017 ◽  
Vol 2 (2) ◽  
pp. 485-494 ◽  
Author(s):  
M.S. Bruzón ◽  
T.M. Garrido ◽  
R. de la Rosa
Keyword(s):  
Kdv Equation ◽  
Nonlinear Problems ◽  
Mathematical Physics ◽  
Lie Symmetry ◽  
Shallow Waters ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Fifth Order ◽  
Wave Phenomena

AbstractIn this work, Lie symmetry analysis is performed on a generalized fifth-order KdV equation. This equation describes many nonlinear problems with great physical interest in mathematical physics, nonlinear dynamics and plasma physics, among them it is a useful model for the description of wave phenomena in plasma and solid state and internal solitary waves in shallow waters. Group invariant solutions are obtained which allow us to transform the equation into ordinary differential equations. Furthermore, taking into account the conservation laws that the ordinary differential equation admits we reduce the order of the equations. Finally, we obtain some exact solutions.

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