Application of Exp(())-expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations

Abstract

In this paper, we explore new applications of the)) (exp(  -expansion method for finding exact traveling wave solutions of generalized Klein-Gordon Equation and right-handed nc-Burgers equation. By means of this method three new solutions of each equations is obtained including the hyperbolic functions, exponential functions and rational function solutions. The proposed method is very effective, efficient and applicable mathematical tools for nonlinear evolution equations (NLEEs). So this method can be used for many other nonlinear evolution equations.

Exact Solutions to the (2+1)-Dimensional Boussinesq Equation via exp(?(?))-Expansion Method

“…We refer to [40][41][42][43] for more details. The nonlinear wave and evolution equations we want to investigate are commonly written as…”

“…complex hyperbolic function method [5,6], the rank analysis method [7], the ansatz method [8,9], the (G′/G)-expansion method [10][11][12][13][14][15][16][17][18][19][20][21], the exp-functions method [22], the modified simple equation method [23,24], the Jacobi elliptic function expansion method [25,26], the Adomian decomposition method [27,28], the homogeneous balance method [29][30][31], the F-expansion method [32,33], the Backlund transformation method [34], the Darboux transformation method [35], the homotopy perturbation method [36,37], the generalized Riccati equation method [38], the tanh-coth method [39], the exp(-φ(η))-expansion method [40][41][42][43] and so on.…”