Lie symmetry analysis, explicit solutions and conservation laws of the time fractional Clannish Random Walker’s Parabolic equation

2020 ◽  
pp. 2150074
Author(s):  
Panpan Wang ◽  
Wenrui Shan ◽  
Ying Wang ◽  
Qianqian Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we mainly study the symmetry analysis and conservation laws of the time fractional Clannish Random Walker’s Parabolic (CRWP) equation. The vector fields and similarity reduction of the time fractional CRWP equation are obtained. In addition, based on the power series theory, a simple and effective approach for constructing explicit power series solutions is proposed. Finally, by use of the new conservation theorem, the conservation laws of the time fractional CRWP equation are constructed.

scholarly journals Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2434
Author(s):  
Ruixin Li ◽  
Lianzhong Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Time Dependent ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Gardner Equation ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation, and then the power series solutions in some specific cases are obtained. By virtue of the fractional conservation theorem, the conservation laws are constructed.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations

2017 ◽  
Vol 72 (3) ◽  
pp. 269-279 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Shou-Fu Tian ◽  
Chun-Yan Qin ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Wave Equations ◽  
Boussinesq Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
Bidirectional Propagation

AbstractIn this article, a generalised Whitham–Broer–Kaup–Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham–Broer–Kaup–Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

scholarly journals A Lie Symmetry Solutions of Sawada-Kotera Equation

2019 ◽  
Vol 17 ◽  
pp. 1-11
Author(s):  
Winny Chepngetich Bor ◽  
Owino M. Oduor ◽  
John K. Rotich
Keyword(s):  
Power Series ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Symmetry Groups ◽  
Series Solutions ◽  
Invariant Solutions ◽  
Infinitesimal Transformation ◽  
Lie Symmetry Analysis ◽  
Power Series Solutions ◽  
Fifth Order

In this article, the Lie Symmetry Analysis is applied in finding the symmetry solutions of the fifth order Sawada-Kotera equation. The technique is among the most powerful approaches currently used to achieveprecise solutions of the partial differential equations that are nonlinear. We systematically show the procedure to obtain the solution which is achieved by developing infinitesimal transformation, prolongations, infinitesimal generatorsand invariant transformations hence symmetry solutions of the fifth order Sawada-Kotera equation. Key Words- Lie symmetry analysis. Sawada-Kotera equation. Symmetry groups. Prolongations. Invariant solutions. Power series solutions. Symmetry solutions.

Lie symmetry analysis, conservation laws and some exact solutions of the time-fractional Buckmaster equation

2020 ◽  
Vol 17 (03) ◽  
pp. 2050040
Author(s):  
Mahdieh Yourdkhany ◽  
Mehdi Nadjafikhah ◽  
Megerdich Toomanian
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Fractional Derivatives ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Power Series Solutions ◽  
Liouville Fractional Derivative

This paper systematically investigates the Lie symmetry analysis of the time-fractional Buckmaster equation in the sense of Riemann–Liouville fractional derivative. With the aid of infinitesimal symmetries, this equation is transformed into a nonlinear ordinary differential equation of fractional order (FODE), where the fractional derivatives are in Erdelyi–Kober sense. The reduced FODE is solved with the explicit power series method and some figures for the obtained power series solutions are also depicted. Finally, Ibragimov’s method and Noether’s theorem have been employed to conclude the conservation laws of this equation.

Symmetry reductions, explicit solutions, convergence analysis and conservation laws via multipliers approach to the Chen–Lee–Liu model in nonlinear optics

2019 ◽  
Vol 33 (04) ◽  
pp. 1950035 ◽  
Author(s):  
Aliyu Isa Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Mustafa Bayram ◽  
Dumitru Baleanu
Keyword(s):  
Nonlinear Optics ◽  
Power Series ◽  
Conservation Laws ◽  
Convergence Analysis ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Series Solutions ◽  
Symmetry Reductions ◽  
Power Series Solutions

In this paper, symmetry analysis is performed for the nonlinear Chen–Lee–Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach.

Symmetry analysis with similarity reduction, new exact solitary wave solutions and conservation laws of (3 + 1)-dimensional extended quantum Zakharov–Kuznetsov equation in quantum physics

2021 ◽  
pp. 2150163
Author(s):  
Vinita ◽  
S. Saha Ray
Keyword(s):  
Conservation Laws ◽  
Quantum Physics ◽  
Physical Structure ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Similarity Reduction ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach ◽  
Conservation Theorem

A recently defined (3+1)-dimensional extended quantum Zakharov–Kuznetsov (QZK) equation is examined here by using the Lie symmetry approach. The Lie symmetry analysis has been used to obtain the varieties in invariant solutions of the extended Zakharov–Kuznetsov equation. Due to existence of arbitrary functions and constants, these solutions provide a rich physical structure. In this paper, the Lie point symmetries, geometric vector field, commutative table, symmetry groups of Lie algebra have been derived by using the Lie symmetry approach. The simplest equation method has been presented for obtaining the exact solution of some reduced transform equations. Finally, by invoking the new conservation theorem developed by Nail H. Ibragimov, the conservation laws of QZK equation have been derived.

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

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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