Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation

Md Hamidul Islam; Kamruzzaman Khan; M Ali Akbar; Md Abdus Salam

doi:10.1186/2193-1801-3-105

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation

Springerplus. 2014 Feb 21:3:105. doi: 10.1186/2193-1801-3-105. eCollection 2014.

Authors

Md Hamidul Islam¹, Kamruzzaman Khan², M Ali Akbar³, Md Abdus Salam⁴

Affiliations

¹ Department of Electronics and Telecommunication Engineering, Prime University, Dhaka, 1216 Bangladesh ; School of Biomolecular and Physical Sciences, Griffith University, Kragujevac, Australia.
² Department of Mathematics, Pabna University of Science and Technology, Pabna, 6600 Bangladesh.
³ Department of Applied Mathematics, University of Rajshahi, Rajshahi, 6205 Bangladesh.
⁴ Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail, 1902 Bangladesh.

Abstract

Abstract: Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters.

Mathematics subject classification: 35C07; 35C08; 35P99.

Keywords: Enhanced (G '/G)-expansion method; Modified KDV-ZK equation; Solitary wave; Traveling wave; Viscous burgers equation.