On New Conservation Laws of Fin Equation

We study the new conservation forms of the nonlinear fin equation in mathematical physics. In this study, first, Lie point symmetries of the fin equation are identified and classified. Then by using the relationship of Lie symmetry andλ-symmetry, newλ-functions are investigated. In addition, the Jacobi Last Multiplier method and the approach, which is based on the factλ-functions are assumed to be of linear form, are considered as different procedures for lambda symmetry analysis. Finally, the corresponding new conservation laws and invariant solutions of the equation are presented.

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Symmetry Solutions and Conservation Laws for the 3D Generalized Potential Yu-Toda-Sasa-Fukuyama Equation of Mathematical Physics

Symmetry ◽

10.3390/sym13112058 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2058

Author(s):

Chaudry Masood Khalique ◽

Karabo Plaatjie ◽

Oageng Lawrence Diteho

Keyword(s):

Conservation Laws ◽

Elliptic Integral ◽

Three Dimensional ◽

Mathematical Physics ◽

Lie Point Symmetries ◽

Invariant Solutions ◽

Conservation Of Energy ◽

Group Invariant ◽

Generalized Potential ◽

Group Invariant Solutions

In this paper we study the fourth-order three-dimensional generalized potential Yu-Toda-Sasa-Fukuyama (gpYTSF) equation by first computing its Lie point symmetries and then performing symmetry reductions. The resulting ordinary differential equations are then solved using direct integration, and exact solutions of gpYTSF equation are obtained. The obtained group invariant solutions include the solution in terms of incomplete elliptic integral. Furthermore, conservation laws for the gpYTSF equation are derived using both the multiplier and Noether’s methods. The multiplier method provides eight conservation laws, while the Noether’s theorem supplies seven conservation laws. These conservation laws include the conservation of energy and mass.

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

Symmetry ◽

10.3390/sym12081378 ◽

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.

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

Symmetry ◽

10.3390/sym11070840 ◽

2019 ◽

Vol 11 (7) ◽

pp. 840 ◽

Cited By ~ 1

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.

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Symmetry analysis and conservation laws of the time fractional Kaup-Kupershmidt equation from capillary gravity waves

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2018025 ◽

2018 ◽

Vol 13 (2) ◽

pp. 24

Author(s):

Zhonglong Zhao ◽

Bo Han

Keyword(s):

Conservation Laws ◽

Gravity Waves ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Lie Point Symmetries ◽

Lie Symmetry Analysis ◽

Similarity Reduction

The Lie symmetry analysis is employed to study the time fractional Kaup-Kupershmidt equation from capillary gravity waves. The Lie point symmetries and the similarity reduction of this equation are obtained. Then we construct the conservation laws by means of Ibragimov’s method.

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Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation

Open Physics ◽

10.1515/phys-2018-0042 ◽

2018 ◽

Vol 16 (1) ◽

pp. 302-310 ◽

Cited By ~ 21

Author(s):

Dumitru Baleanu ◽

Mustafa Inc ◽

Abdullahi Yusuf ◽

Aliyu Isa Aliyu

Keyword(s):

Conservation Laws ◽

Nonlinear Ordinary Differential Equation ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Lie Point Symmetries ◽

Fractional Partial Differential Equations ◽

Lie Symmetry Analysis ◽

Kawahara Equation ◽

Power Series Technique ◽

Series Technique

AbstractIn this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.

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