scholarly journals SOLITARY WAVE SOLUTIONS TO THE 2N+1 ORDER KdV-TYPE EQUATIONS

1996 ◽  
Vol 45 (11) ◽  
pp. 1777
Author(s):  
ZHU ZUO-NONG
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
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

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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