scholarly journals The Basic (<i>G'/G</i>)-Expansion Method for the Fourth Order Boussinesq Equation

2012 ◽  
Vol 03 (10) ◽  
pp. 1144-1152 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Expansion Method

scholarly journals Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

scholarly journals A Fourth Order Finite Difference Method for the Good Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
M. S. Ismail ◽  
Farida Mosally
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
First Order ◽  
System A ◽  
Accuracy And Stability ◽  
Linearization Techniques

The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.

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