On new traveling wave solutions of potential KdV and (3+1)-dimensional Burgers equations

Volume 9, Issue 7, pp 5029--5040 http://dx.doi.org/10.22436/jnsa.009.07.07

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Authors

Fairouz Tchier - Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia. Ibrahim E. Inan - Faculty of Education, Firat University, 23119 Elazig, Turkey. Yavuz Ugurlu - Science Faculty, Department of Mathematics, Firat University, 23119 Elazig, Turkey. Mustafa Inc - Science Faculty, Department of Mathematics, Firat University, 23119 Elazig, Turkey. Dumitru Baleanu - Department of Mathematics, Cankaya University, Ogretmenler Cad. 14 06530, Balgat, Ankara, Turkey. - Institute of Space Sciences, Magurele-Bucharest, Romania.

Abstract

This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables \((\frac{G'}{ G} ,\frac{ 1}{ G})\) expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena.

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Keywords

• \((\frac{G'}{ G}، \frac{ 1}{ G})\) -EM
• the PKdV equation
• the (3+1)-dimensional BE
• hyperbolic solution
• periodic solution
• rational solution.

MSC

•  35Q53
•  35C08
•  35C07

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