Bifurcations and exact traveling wave solutions for a class of nonlinear fourth-order partial differential equations

2014 ◽  
Vol 80 (1-2) ◽  
pp. 129-145 ◽  
Author(s):  
Liyan Zhong ◽  
Shengqiang Tang ◽  
Lijing Qiao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

Exact traveling wave solutions of partial differential equations with power law nonlinearity

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
H. Aminikhah ◽  
B. Pourreza Ziabary ◽  
H. Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Hyperbolic Function ◽  
Mathematical Tool ◽  
Partial Differential ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

AbstractIn this paper, we applied the functional variable method for four famous partial differential equations with power lawnonlinearity. These equations are included the Kadomtsev-Petviashvili, (3+1)-Zakharov-Kuznetsov, Benjamin-Bona-Mahony-Peregrine and Boussinesq equations. Various exact traveling wave solutions of these equations are obtained that include the hyperbolic function solutions and the trigonometric function solutions. The solutions shown that this method provides a very effective, simple and powerful mathematical tool for solving nonlinear equations in various fields of applied sciences.

scholarly journals Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Rational Solutions ◽  
Partial Differential ◽  
Wave Solutions

We apply the G′/G2-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

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