scholarly journals Travelling wave solutions of nonlinear systems of PDEs by using the functional variable method

2015 ◽  
Vol 34 (2) ◽  
pp. 213-229 ◽  
Author(s):  
Hossein Aminikhah ◽  
Amir Hosein Refahi Sheikhani ◽  
Hadi Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Travelling Wave ◽  
Variable Method ◽  
Boussinesq System ◽  
Wave Transformation ◽  
Partial Differential ◽  
Functional Variable ◽  
Functional Variable Method

In this paper, we will use the functional variable method to construct exact solutions of some nonlinear systems of partial differential equations, including, the (2+1)-dimensional Bogoyavlenskii’s breaking soliton equation, the WhithamBroer-Kaup-Like systems and the Kaup-Boussinesq system. This approach can also be applied to other nonlinear systems of partial differential equations which can be converted to a second-order ordinary differential equation through the travelling wave transformation.

scholarly journals Novel Exact Solutions of the Extended Shallow Water Wave and the Fokas Equations

2018 ◽  
Vol 22 ◽  
pp. 01022
Author(s):  
Serbay DURAN ◽  
Berat KARAAGAC ◽  
Alaattin ESEN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Expansion Method ◽  
Travelling Wave ◽  
Wave Transformation ◽  
Partial Differential ◽  
Shallow Water Wave

In this study, a Sine-Gordon expansion method for obtaining novel exact solutions of extended shallow water wave equation and Fokas equation is presented. All of the equations which are under consideration consist of three or four variable. In this method, first of all, partial differential equations are reduced to ordinary differential equations by the help of variable change called as travelling wave transformation, then Sine Gordon expansion method allows us to obtain new exact solutions defined as in terms of hyperbolic trig functions of considered equations. The newly obtained results showed that the method is successful and applicable and can be extended to a wide class of nonlinear partial differential equations.

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