Geometrical Properties and Exact Solutions of Three (3+1)-Dimensional Nonlinear Evolution Equations in Mathematical Physics Using Different Expansion Methods
A. R. Shehata *
Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt.
Safaa S. M. Abu-Amra
Department of Mathematics, Faculty of Science, Omar Al-Mukhtar University, Al-Bayda, Libya.
*Author to whom correspondence should be addressed.
Abstract
In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics.
In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics.
Keywords: Travelling wave solutions, variation (G'⁄G)-expansion method, (G'/G2)-expansion method, nonlinear evolution equations