Abstract
Exact solutions of nonlinear evolution equations (NLEEs) play very important role to make known the inner mechanism of compound physical phenomena. In this paper, the new generalized (G'/G)-expansion method is used for constructing the new exact traveling wave solutions for some nonlinear evolution equations arising in mathematical physics namely, the (3+1)-dimensional Zakharov-Kuznetsov equation and the Burgers equation. As a result, the traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. This method is very easy, direct, concise and simple to implement as compared with other existing methods. This method presents a wider applicability for handling nonlinear wave equations. Moreover, this procedure reduces the large volume of calculations.
Highlights
The investigation of the travelling wave solutions for nonlinear partial differential equations plays an important role in the study of nonlinear physical phenomena
We obtain further new exact traveling wave solutions T22 (η), T24 (η), T26 (η) − T29 (η), T11 (η) − T19 (η), T31 (η) − T39 (η) in this article, which have not been reported in the previous literature
Some new exact traveling wave solutions of the (3+1)-dimensional Zakharov-Kuznetsov equation and the Burgers equation are constructed in this article by applying the new generalized (G′ / G) -expansion method
Summary
The investigation of the travelling wave solutions for nonlinear partial differential equations plays an important role in the study of nonlinear physical phenomena. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. The Burgers equation is used to capture some of the features of turbulent fluid in a channel caused by the interaction of the opposite effects of convection and diffusion. The (3+1)-dimensional Zakharov–Kuznetsov equation describes weakly nonlinear wave process in dispersive and isotropic media e.g., waves in magnetized plasma or water waves in shear flows
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
