Lie symmetry analysis to the time fractional generalized fifth-order KdV equation

2013 ◽  
Vol 18 (9) ◽  
pp. 2321-2326 ◽  
Author(s):  
Gang-wei Wang ◽  
Xi-qiang Liu ◽  
Ying-yuan Zhang
Keyword(s):  
Kdv Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Fifth Order

scholarly journals Symmetry Reductions for a Generalized Fifth Order KdV Equation

2017 ◽  
Vol 2 (2) ◽  
pp. 485-494 ◽  
Author(s):  
M.S. Bruzón ◽  
T.M. Garrido ◽  
R. de la Rosa
Keyword(s):  
Kdv Equation ◽  
Nonlinear Problems ◽  
Mathematical Physics ◽  
Lie Symmetry ◽  
Shallow Waters ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Fifth Order ◽  
Wave Phenomena

AbstractIn this work, Lie symmetry analysis is performed on a generalized fifth-order KdV equation. This equation describes many nonlinear problems with great physical interest in mathematical physics, nonlinear dynamics and plasma physics, among them it is a useful model for the description of wave phenomena in plasma and solid state and internal solitary waves in shallow waters. Group invariant solutions are obtained which allow us to transform the equation into ordinary differential equations. Furthermore, taking into account the conservation laws that the ordinary differential equation admits we reduce the order of the equations. Finally, we obtain some exact solutions.

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.

On the Lie symmetry analysis and traveling wave solutions of time fractional fifth-order modified Sawada-Kotera equation

2018 ◽  
pp. 411-416 ◽  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Derivative Operator ◽  
Order Ordinary Differential Equation ◽  
Lie Group Theory ◽  
Liouville Derivative ◽  
Fifth Order

In this paper, we study Lie symmetry analysis of the time fractional fifth-order modified Sawada-Kotera equation (FMSK) with Riemann-Liouville derivative. Applying the adapted the Lie group theory to the equation under study, two dimensional Lie algebra is deduced. Using the obtained nontrivial Lie point symmetry, it is shown that the equation can be converted into a nonlinear fifth order ordinary differential equation of fractional order in the meaning of the Erdelyi-Kober fractional derivative operator. In addition, we construct some exact traveling solutions for the FMSK using the sub-equation method.

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