﻿ The (G’/G)-Expansion Method and Traveling Wave Solutions for Some Nonlinear PDEs
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### The (G’/G)-Expansion Method and Traveling Wave Solutions for Some Nonlinear PDEs

J.F. Alzaidy
Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia
American Journal of Mathematical Analysis. 2013, 1(3), 28-32. DOI: 10.12691/ajma-1-3-1
Published online: August 25, 2017

### Abstract

In the present paper, we construct the traveling wave solutions involving parameters of some nonlinear PDEs in mathematical physics via the nonlinear SchrÖdinger (NLS−) equation and the regularized long-wave (RLW) equation by using a simple method which is called the (G’/G) -expansion method, where G=G(ζ) satisfies the second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear PDEs arising in mathematical physics.

### Keywords:

the (G’/G) -expansion method, traveling wave solutions, nonlinear SchrÖdinger (NLS−) equation, regularized long-wave (RLW) equation, solitary wave solutions
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