scholarly journals Exploration on traveling wave solutions to the 3rd-order klein–fock-gordon equation (KFGE) in mathematical physics

2020 ◽  
Vol 8 (1) ◽  
pp. 14 ◽  
Author(s):  
Nur Hasan Mahmud Shahen ◽  
Foyjonnesa . ◽  
Md. Habibul Bashar
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Dynamic Models ◽  
Gordon Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Analytic Solutions ◽  
Hyperbolic Function ◽  
Wave Solutions

In this paper, the -expansion method has been applied to find the new exact traveling wave solutions of the nonlinear evaluation equations (NLEEs) by utilizing 3rd-order Klein–Gordon Equation (KFGE). With the collaboration of symbolic commercial software maple, the competence of this method for inventing these exact solutions has been more exhibited. As an upshot, some new exact solutions are obtained and signified by hyperbolic function solutions, different combinations of trigonometric function solutions, and exponential function solutions. Moreover, the -expansion method is a more efficient method for exploring essential nonlinear waves that enrich a variety of dynamic models that arises in nonlinear fields. All sketching is given out to show the properties of the innovative explicit analytic solutions. Our proposed method is directed, succinct, and reasonably good for the various nonlinear evaluation equations (NLEEs) related treatment and mathematical physics also. 

Geometrical Properties and Exact Solutions of Three (3+1)-Dimensional Nonlinear Evolution Equations in Mathematical Physics Using Different Expansion Methods

2019 ◽  
pp. 1-19
Author(s):  
A. R. Shehata ◽  
Safaa S. M. Abu-Amra
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Shallow Water Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions

In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics. In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) 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 Further Results about Traveling Wave Exact Solutions of the Drinfeld-Sokolov Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Fu Zhang ◽  
Jian-ming Qi ◽  
Wen-jun Yuan
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
Wave Solutions ◽  
Periodic Traveling Wave

We employ the complex method to obtain all meromorphic exact solutions of complex Drinfeld-Sokolov equations (DS system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all constant and simply periodic traveling wave exact solutions of the equations (DS) are solitary wave solutions, the complex method is simpler than other methods and there exist simply periodic solutionsvs,3(z)which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

scholarly journals New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Ginzburg Landau ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

Application of Improved (G′/G)–Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations

2012 ◽  
Vol 4 (1) ◽  
pp. 122-130 ◽  
Author(s):  
Xiaohua Liu ◽  
Weiguo Zhang ◽  
Zhengming Li
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
The Other ◽  
Wave Solutions

AbstractIn this work, the improved (G′/G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation. In order to illustrate the validity of the method we choose the RLW equation and SRLW equation. As a result, many new and more general exact solutions have been obtained for the equations. We will compare our solutions with those gained by the other authors.

scholarly journals Traveling Wave Solutions of Nonlinear Evolution Equation via Enhanced(G’/G)- Expansion Method

2014 ◽  
Vol 33 ◽  
pp. 83-92 ◽  
Author(s):  
Md. Ekramul Islam ◽  
Kamruzzaman Khan ◽  
M Ali Akbar ◽  
Rafiqul Islam
Keyword(s):  
Rational Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Wave Solutions

In this article, the Enhanced (G'/G)-expansion method has been projected to find the traveling wave solutions for nonlinear evolution equations(NLEEs) via the (2+1)-dimensional Burgers equation. The efficiency of this method for finding these exact solutions has been demonstrated with the help of symbolic computation software Maple. By this method we have obtained many new types of complexiton soliton solutions, such as, various combinations of trigonometric periodic function and rational function solutions, various combination of hyperbolic function and rational function solutions. The proposed method is direct, concise and effective, and can be used for many other nonlinear evolution equations. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 83-92 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17662

scholarly journals Applications of an Extended -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
E. M. E. Zayed ◽  
Shorog Al-Joudi
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Expansion Method ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Soliton Equation ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Hyperbolic Function Solutions

We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended -expansion method, whereGsatisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

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