scholarly journals KINK-BRIGHT SOLITARY WAVE SOLUTIONS OF THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION

2021 ◽  
Vol 33 (1) ◽  
pp. 59-80
Author(s):  
Hugues Martial Omanda ◽  
Gaston N’tchayi Mbourou ◽  
Clovis Taki Djeumen Tchaho ◽  
Jean Roger Bogning
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Sivashinsky Equation

Application of Optimal Homotopy Analysis Method for Solitary Wave Solutions of Kuramoto-Sivashinsky Equation

2011 ◽  
Vol 66 (1-2) ◽  
pp. 117-122
Author(s):  
Qi Wang
Keyword(s):  
Solitary Wave ◽  
Homotopy Analysis Method ◽  
Solitary Wave Solutions ◽  
Analysis Method ◽  
Convergence Region ◽  
Optimal Method ◽  
Optimal Homotopy Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis ◽  
Sivashinsky Equation

In this paper, the optimal homotopy analysis method is applied to find the solitary wave solutions of the Kuramoto-Sivashinsky equation. With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with a simple way to adjust and control the convergence region of the solution. Compared with the usual homotopy analysis method, the optimal method can be used to get much faster convergent series solutions.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

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