Abstract
In this Letter, the (G'/G) -expansion method is proposed to seek exact solutions of nonlinear evolution equations. For illustrative examples, we choose the compound KdV-Burgers equation, the compound KdV equation, the KdV-Burgers equation, the mKdV equation. The power of the employed method is confirmed.
Highlights
Nonlinear evolution equations (NLEEs) have been the subject of study in various branches of mathematical–physical sciences such as physics, biology, chemistry, etc
The analytical solutions of such equations are of fundamental importance since a lot of mathematical–physical models are described by NLEEs
In recent years, searching for explicit solutions of NLEEs by using various methods has become the main goal for many authors
Summary
Nonlinear evolution equations (NLEEs) have been the subject of study in various branches of mathematical–physical sciences such as physics, biology, chemistry, etc. Many powerful methods to construct exact solutions of NLEEs have been established and developed 1 10. Wang et al 11 introduced an expansion technique called the G / G -expansion method and they demonstrated that it is powerful technique for seeking analytic solutions of nonlinear partial differential equations. Our aim in this paper is to present an application of the G / G -expansion method to the compound KdV–Burgers-type equations. Seek traveling wave solutions of Eq 1 by taking u x,t U , x Vt , where V is the wave speed, and transform Eq 1 to the ordinary differential equation. Integrate Eq 2 term by term one or more times. The function G is the solution of the auxiliary linear ordinary differential equation
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