Exp-Function Method for Solving Nonlinear Evolution Equations

Abstract

Abstract-In this paper, we applied Exp-function method to some nonlinear evolution equations. The solution procedure of this method, by the help of symbolic computation of Matlab, Mathematica or so on, is of utter simplicity. The obtained results show that Exp-function method is very powerful and convenient mathematical tool for nonlinear evolution equations in science and engineering.

Numerical experiments with the Bratu equation in one, two and three dimensions

“…The two-dimensional case is more complicated and analytical solutions are not known. It was studied numerically (Boyd 1986;Misirli and Gurefe 2011;Kapania 1990) and we verify and generalize the existing results. The three-dimensional case is examined, to our knowledge, for the first time and our results are novel.…”

On the exact solutions of high order wave equations of KdV type (I)

“…For a given nonlinear partial differential equation; P(u, u t , u x , u xx , · · · ) = 0, (2) take the wave transformation…”

An efficient technique for higher order fractional differential equation

“…The investigation of travelling wave solutions (Shawagfeh 2002; Ray and Bera 2005; Yildirim et al 2011; Kilbas et al 2006; He and Li 2010; Momani and Al-Khaled 2005; Odibat and Momani 2007; Abdou 2007; Nassar et al 2011; Misirli and Gurefe 2011; Noor et al 2008; Ozis and Koroglu 2008; Wu and He 2007; Yusufoglu 2008; Zhang 2007; Zhu 2007; Wang et al 2008; Zayed et al 2004; Sirendaoreji 2004; Ali 2011; Liang et al 2011; He et al 2012; Jawad et al 2010; Zhou et al 2003; Yıldırım and Kocak 2009; Elbeleze et al 2013; Matinfar and Saeidy 2010; Ahmad 2014; Bongsoo 2009; Demiray and Pandir 2014, 2015; Lu 2012; Zayed and Amer 2014) of nonlinear evolution equations plays a significant role to look into the internal mechanism of nonlinear physical phenomena. Nonlinear fractional differential equations (FDEs) are a generalization of classical differential equations of integer order.…”