scholarly journals Abundant general solitary wave solutions to the family of KdV type equations

2017 ◽  
Vol 2 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Md. Azmol Huda ◽  
M. Ali Akbar ◽  
Shewli Shamim Shanta
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Family ◽  
Kdv Type Equations

scholarly journals Solitary wave solutions of two KdV-type equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 311-318 ◽  
Author(s):  
Khalil Salim Al-Ghafri
Keyword(s):  
Solitary Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Dispersive Equation ◽  
Wave Solutions ◽  
Kdv Type Equations ◽  
Projective Riccati Equation Method

AbstractThe present paper investigates the solitary wave solutions of the nonlinear evolution equations with power nonlinearties. The study has been carried out for two examples of KdV-type equations, namely, the nonlinear dispersive equation and the generalised KdV equation. To achieve our goal, we have applied the projective Riccati equation method. As a result, many exact solutions in the form of solitary wave solutions and combined formal solitary wave solutions are obtained

Abundant solitary wave solutions for the fractional coupled Jaulent–Miodek equations arising in applied physics

2020 ◽  
Vol 34 (29) ◽  
pp. 2050279
Author(s):  
Asim Zafar ◽  
Ahmet Bekir ◽  
Bushra Khalid ◽  
Hadi Rezazadeh
Keyword(s):  
Solitary Wave ◽  
Wave Equations ◽  
Solitary Wave Solutions ◽  
Applied Physics ◽  
Coupled Equations ◽  
Integration Schemes ◽  
Wave Solutions ◽  
Shallow Water Wave Equations ◽  
The Family ◽  
First Time

This article explores the abundant solitary wave solutions of the conformable coupled Jaulent–Miodek (JM) equations appearing in applied physics. The aforesaid coupled equations belong to the family of shallow-water wave equations. Two recent modified integration schemes are used for the first time to produce a novel solitary wave, trigonometric and other solutions with some free parameters in the conformable derivative sense. In particular, the modified Kudryashov and [Formula: see text]-expansion schemes are used to illustrate the wave propagations through aforesaid solutions of the JM equations. Furthermore, a comparison is made with some recent results and the dynamics of the obtained solutions are displayed for the reader via soft computation. The outcomes reveal that the methods are effective and provide a direct way of finding novel 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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