Lie symmetry analysis, conservation laws and similarity reductions of Newell–Whitehead–Segel equation of fractional order

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 11

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.

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

Complexity ◽

10.1155/2020/4830684 ◽

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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Conservation Laws and Exact Series Solution of Fractional-Order Hirota-Satsoma Coupled KdV system by Symmetry Analysis

10.22541/au.162223020.00263781/v1 ◽

2021 ◽

Author(s):

Hemant Gandhi ◽

Amit Tomar ◽

Dimple Singh

Keyword(s):

Conservation Laws ◽

Fractional Order ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Lie Symmetry Analysis ◽

Infinitesimal Generators ◽

Coupled Equations ◽

Fractional Differential ◽

Power Series Technique ◽

Series Technique

In this work, we investigated the invariance analysis of fractional-order Hirota-Satsoma coupled Korteveg-de-Vries (HSC-KdV) system of equations based on Riemann-Liouville (RL) derivatives. The Lie Symmetry analysis is considered to obtain infinitesimal generators; we reduced the system of coupled equations into nonlinear fractional ordinary differential equations (FODEs) with the help of Erdelyi’s-Kober (EK) fractional differential and integral operators. The reduced system of FODEs solved by means of the power series technique with its convergence. The conservation laws of the system constructed by Noether’s theorem.

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

Advances in Mathematical Physics ◽

10.1155/2021/9113423 ◽

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.

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Lie symmetry reductions and conservation laws for fractional order coupled KdV system

Advances in Difference Equations ◽

10.1186/s13662-020-03149-z ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Hossein Jafari ◽

Hong Guang Sun ◽

Marzieh Azadi

Keyword(s):

Conservation Laws ◽

Fractional Order ◽

Lie Symmetry ◽

Theoretical Physics ◽

Lie Symmetry Analysis ◽

Kdv Equations ◽

Ode System ◽

Coupled Kdv Equations ◽

Scientific Phenomena ◽

New System

AbstractLie symmetry analysis is achieved on a new system of coupled KdV equations with fractional order, which arise in the analysis of several problems in theoretical physics and numerous scientific phenomena. We determine the reduced fractional ODE system corresponding to the governing factional PDE system.In addition, we develop the conservation laws for the system of fractional order coupled KdV equations.

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