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, Exact Solutions, Conservation Laws and Bäcklund Transformations of the Gibbons-Tsarev Equation

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1378
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
The Self ◽  
Bäcklund Transformations ◽  
Invariant Solutions ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Parameter Transformation ◽  
Backlund Transformations

In this paper, we mainly put the Lie symmetry analysis method on the Gibbons-Tsarev equation (GTe) to obtain some new results, including some Lie symmetries, one-parameter transformation groups, explicit invariant solutions in the form of power series. Subsequently, the self-adjointness of the GTe is singled out. It follows that the conservation laws associated with symmetries of GTe are constructed with the aid of Ibragimov’ method. Finally, we present the Bäcklund transformations so that more abundant solutions can be worked out.

scholarly journals Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Similarity Reductions

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid ofG′/G-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

scholarly journals Lie symmetry analysis of some time fractional partial differential equations

2015 ◽  
Vol 38 ◽  
pp. 1560075 ◽  
Author(s):  
E. H. El Kinani ◽  
A. Ouhadan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Fractional Partial Differential Equations ◽  
Lie Symmetry Analysis ◽  
Partial Differential ◽  
Independent Variables ◽  
Symmetry Properties

This paper uses Lie symmetry analysis to reduce the number of independent variables of time fractional partial differential equations. Then symmetry properties have been employed to construct some exact solutions.

scholarly journals Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Baoyong Guo ◽  
Huanhe Dong ◽  
Yong Fang
Keyword(s):  
Conservation Laws ◽  
Differential Operators ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Symmetry Groups ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Reduced Equations ◽  
Liouville Fractional Derivative ◽  
Similarity Reductions

In this paper, the time-fractional Fujimoto–Watanabe equation is investigated using the Riemann–Liouville fractional derivative. Symmetry groups and similarity reductions are obtained by virtue of the Lie symmetry analysis approach. Meanwhile, the time-fractional Fujimoto–Watanabe equation is transformed into three kinds of reduced equations and the third of which is based on Erdélyi–Kober fractional integro-differential operators. Furthermore, the conservation laws are also acquired by Ibragimov’s theory.

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