Abstract
In this article, we apply the modified (G'/G)-expansion method to construct hyperbolic, trigonometric and rational function solutions of nonlinear evolution equations. This method can be thought of as the generalization of the (G'/G)-expansion method given recently by Wang et al. (2008). To illustrate the validity and advantages of this method, the (1+1)-dimensional Hirota-Ramani equation and the (2+1)-dimensional breaking soliton equation are considered and more general traveling wave solutions are obtained. It is shown that the proposed method provides a more general powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Key words: Nonlinear evolution equations, modified (G'/G)-expansion method, hyperbolic Function solutions, trigonometric function solutions, rational function solutions.
Highlights
Nonlinear evolution equations are often presented to describe the motion of isolated waves, localized in a small part of space, in many fields such as hydrodynamics, plasma physics, and nonlinear optics
It is shown that the proposed method provides a more general powerful mathematical tool for solving nonlinear evolution equations in mathematical physics
Wang et al (2008) introduced the (G'/G)-expansion method to look for traveling wave solutions of nonlinear evolution equations
Summary
The modified (G'/G)-expansion method for the (1+1) Hirota-Ramani and (2+1) breaking soliton equation. We apply the modified (G'/G)-expansion method to construct hyperbolic, trigonometric and rational function solutions of nonlinear evolution equations. This method can be thought of as the generalization of the (G'/G)-expansion method given recently by Wang et al (2008). To illustrate the validity and advantages of this method, the (1+1)-dimensional Hirota-Ramani equation and the (2+1)dimensional breaking soliton equation are considered and more general traveling wave solutions are obtained. It is shown that the proposed method provides a more general powerful mathematical tool for solving nonlinear evolution equations in mathematical physics
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