The Investigation of Exact Solutions of Korteweg-de Vries Equation with Dual Power Law Nonlinearity using the expa and exp(-ɸ(ξ)) Methods

2021 ◽  
pp. 1-14
Author(s):  
Ghazala Akram ◽  
Naila Sajid
Keyword(s):  
Exact Solutions ◽  
Power Law ◽  
Vries Equation ◽  
De Vries ◽  
Dual Power

Analytical study of exact solutions of the nonlinear Korteweg–de Vries equation with space–time fractional derivatives

2018 ◽  
Vol 32 (02) ◽  
pp. 1850012 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Space Time ◽  
Strong Basis ◽  
De Vries

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg–de Vries equation with space–time local fractional derivatives. By using the improved [Formula: see text]-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

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