Exact Solutions For some nonlinear Partial Differential Equations by A Variation of (๐‘ฎโ€ฒ๐‘ฎโ„)-Expansion Method:

Document Type : Research Articles

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1 Department of Mathematics, Faculty of Science, Minia University, 61519 Minia, Egypt

2 Department of Mathematics Faculty of Science, Omar Al-Mukhtar University, Al-Bayda. Libya

Abstract

In this article , we study exact solutions of nonlinear of Burger’s Equation, Symmetric Regularized Long Wave (SRLW) equation, and Whitham-Broer-Kaup equations by using the variation of (G'⁄G)-expansion method, respectively. With the aid of mathematical software Maple, we can obtain the exact solutions for the above equations. Here we use the variation of (G'⁄G)-expansion method by applying it to solve the above mentioned equations, some new exact traveling wave solutions are obtained which include solitary wave solutions.When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. It is shown that the methods are effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. This methods is effectual, uncomplicated and can also be used to tackle a number of other differential equations related to mathematical physics

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