Abstract
The novel (G'/G)-expansion method is a powerful and simple technique for finding exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we study explicit exact traveling wave solutions for the (1 + 1)-dimensional combined KdV-mKdV equation by using the novel (G'/G)-expansion method. Consequently, various traveling wave solutions patterns including solitary wave solutions, periodic solutions, and kinks are detected and exhibited.
Highlights
nonlinear evolution equations (NLEEs) arise in a wide variety of disciplines physical problems such as in physics, biology, fluid mechanics, solid-state physics, biophysics, solid mechanics, condensed matter physics, plasma physics, quantum mechanics, optical fibers, elastic media, reaction-diffusion models, and quantum field theory
Worthy is it to note perhaps that rudiments of the (G'/G)-expansion method was used by Eckstein and Belgacem, as early as the late 80’s, to describe the platelet transport behavior in blood vessels, [34]-[36]
The aim of this paper is to find exact and solitary wave solutions of the (1 + 1)-dimensional combined KdV-mKdV equation by the novel (G'/G)-expansion method
Summary
NLEEs arise in a wide variety of disciplines physical problems such as in physics, biology, fluid mechanics, solid-state physics, biophysics, solid mechanics, condensed matter physics, plasma physics, quantum mechanics, optical fibers, elastic media, reaction-diffusion models, and quantum field theory. Many kinds of powerful methods have been proposed to find exact traveling wave solutions of NLEEs e.g., the exp (−Φ (η )) -. How to cite this paper: Alam, Md.N., Belgacem, F.B.M. and Akbar, M.A. (2015) Analytical Treatment of the Evolutionary (1 + 1)-Dimensional Combined KdV-mKdV Equation via the Novel (G'/G)-Expansion Method. Alam and Belgacem in their study appearing in the Waves, Wavelets and Fractals-Abstract Analysis Journal, applied the novel method to the long wave equation, [37]. The aim of this paper is to find exact and solitary wave solutions of the (1 + 1)-dimensional combined KdV-mKdV equation by the novel (G'/G)-expansion method
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