scholarly journals Lie symmetries of Benjamin-Ono equation

2021 ◽  
Vol 18 (6) ◽  
pp. 9496-9510
Author(s):  
Weidong Zhao ◽  
◽  
Mobeen Munir ◽  
Ghulam Murtaza ◽  
Muhammad Athar ◽  
...  
Keyword(s):  
Differential Equation ◽  
Recent Work ◽  
Present Article ◽  
Internal Waves ◽  
Laws Of Nature ◽  
Symmetry Algebra ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
One Dimension ◽  
Lie Symmetry Analysis

<abstract><p>Lie Symmetry analysis is often used to exploit the conservative laws of nature and solve or at least reduce the order of differential equation. One dimension internal waves are best described by Benjamin-Ono equation which is a nonlinear partial integro-differential equation. Present article focuses on the Lie symmetry analysis of this equation because of its importance. Lie symmetry analysis of this equation has been done but there are still some gaps and errors in the recent work. We claim that the symmetry algebra is of five dimensional. We reduce the model and solve it. We give its solution and analyze them graphically.</p></abstract>

scholarly journals Lie Symmetry Analysis of C 1 m , a , b Partial Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Hengtai Wang ◽  
Aminu Ma’aruf Nass ◽  
Zhiwei Zou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Symmetry Algebra ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Invariant Solutions ◽  
Lie Symmetry Analysis ◽  
Low Dimensions ◽  
Similarity Reductions

In this article, we discussed the Lie symmetry analysis of C 1 m , a , b fractional and integer order differential equations. The symmetry algebra of both differential equations is obtained and utilized to find the similarity reductions, invariant solutions, and conservation laws. In both cases, the symmetry algebra is of low dimensions.

scholarly journals Lie Symmetry Analysis of the Hopf Functional-Differential Equation

Symmetry ◽  
2015 ◽  
Vol 7 (3) ◽  
pp. 1536-1566 ◽  
Author(s):  
Daniel Janocha ◽  
Marta Wacławczyk ◽  
Martin Oberlack
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Functional Differential

scholarly journals Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 840 ◽  
Author(s):  
Almudena P. Márquez ◽  
María S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Conservation Laws ◽  
Mechanical Behaviour ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Partial Differential

In this paper, we study a generalization of the well-known Kelvin-Voigt viscoelasticity equation describing the mechanical behaviour of viscoelasticity. We perform a Lie symmetry analysis. Hence, we obtain the Lie point symmetries of the equation, allowing us to transform the partial differential equation into an ordinary differential equation by using the symmetry reductions. Furthermore, we determine the conservation laws of this equation by applying the multiplier method.

scholarly journals Lie Symmetry and Painlevé Test for the SIRD Model

2018 ◽  
Author(s):  
Maba Boniface Matadi
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Invariant Solution ◽  
Symmetry Algebra ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Chaotic Behaviour ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
Infinitesimal Generators

In this paper, Lie symmetry and Painlev&eacute; Techniques are applied to the SIRD (Susceptible, Infected, Recovered and Dead) model. A demonstration of the integrability of the model is provided to present an exact solution. The study revealed that nonlinear system passes Painlev&eacute; test and does not possesses complex chaotic behaviour. However, the system fails to pass the Painlev&eacute; test while constraints reach values equivalent to the corresponding complex chaotic behaviour. The two-dimensional Lie symmetry algebra and the commutator table of the infinitesimal generators are obtained. Lie symmetry analysis serves to linearize the nonlinear system and find the corresponding invariant solution.

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