Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation

Asıf Yokus, Hülya Durur, Hijaz Ahmad and Shao-Wen Yao
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Asıf Yokus: Department of Actuary, Faculty of Science, Firat University, Elazig 23200, Turkey
Hülya Durur: Department of Computer Engineering, Faculty of Engineering, Ardahan University, Ardahan 75000, Turkey
Hijaz Ahmad: Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Mathematics, 2020, vol. 8, issue 6, 1-16

Abstract: In this paper, a new solution process of ( 1 / G ′ ) -expansion and ( G ′ / G , 1 / G ) -expansion methods has been proposed for the analytic solution of the Zhiber-Shabat (Z-S) equation. Rather than the classical ( G ′ / G , 1 / G ) -expansion method, a solution function in different formats has been produced with the help of the proposed process. New complex rational, hyperbolic, rational and trigonometric types solutions of the Z-S equation have been constructed. By giving arbitrary values to the constants in the obtained solutions, it can help to add physical meaning to the traveling wave solutions, whereas traveling wave has an important place in applied sciences and illuminates many physical phenomena. 3D, 2D and contour graphs are displayed to show the stationary wave or the state of the wave at any moment with the values given to these constants. Conditions that guarantee the existence of traveling wave solutions are given. Comparison of ( G ′ / G , 1 / G ) -expansion method and ( 1 / G ′ ) -expansion method, which are important instruments in the analytical solution, has been made. In addition, the advantages and disadvantages of these two methods have been discussed. These methods are reliable and efficient methods to obtain analytic solutions of nonlinear evolution equations (NLEEs).

Keywords: (1/ G ?)-expansion method; the Zhiber-Shabat equation; ( G ?/ G ,1/ G )-expansion method; traveling wave solutions; exact solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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