scholarly journals The Application of the exp⁡(-Φ(ξ))-Expansion Method for Finding the Exact Solutions of Two Integrable Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Naila Sajid ◽  
Ghazala Akram
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Integrable Equation ◽  
Rational Solutions ◽  
Integrable Equations ◽  
Nonlinear Integrable Equation ◽  
Fifth Order

In this article, the exp⁡-Φξ method is connected to search for new hyperbolic, periodic, and rational solutions of (1+1)-dimensional fifth-order nonlinear integrable equation and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. The obtained solutions consist of trigonometric, hyperbolic, rational functions and W-shaped soliton. Furthermore, 3D and 2D graphs are plotted by choosing the suitable values of the parameters involved.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

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.

scholarly journals New Exact Solutions for a Higher Order Wave Equation of KdV Type Using MultipleG′/G-Expansion Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yinghui He
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Type Equation ◽  
Elliptic Functions ◽  
Wave Model ◽  
Rational Functions ◽  
Expansion Method ◽  
Nonlinear Wave Equations ◽  
Mathematical Tool ◽  
New Exact Solutions

TheG′/G-expansion method is a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems. In our work, exact traveling wave solutions of a generalized KdV type equation of neglecting the highest order infinitesimal term, which is an important water wave model, are discussed by theG′/G-expansion method and its variants. As a result, many new exact solutions involving parameters, expressed by Jacobi elliptic functions, hyperbolic functions, trigonometric function, and the rational functions, are obtained. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time. The related results are enriched.

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