Investigation of exact traveling wave solution for the (2+1) dimensional nonlinear evolution equations via modified extended tanh-function method

Abstract

In this study, we have implemented the modified extended tanh-function method to obtain the exact travelling wave solutions for the general (2+1)-dimensional nonlinear evolution equations. By using this method, some travelling wave solutions are successfully obtained and which have been expressed by the trigonometric, hyperbolic and rational functions. These obtained solutions are an appropriate and desirable for instructive specific nonlinear physical phenomena in genuinely nonlinear dynamical systems. The method is an efficient and reliable mathematical tool for solving many nonlinear evolution equations arising in science and engineering problems.

A variety of exact analytical solutions of extended shallow water wave equations via improved (G’/G) -expansion method

“…In the recent past, many researchers have implemented various analytical methods to seek traveling wave solutions of different nonlinear partial differential equations. Many powerful methods have been successfully developed by diverse groups of mathematicians and physicists, such as, Hirota's bilinear method [1], the tanh-function method [2], [3], the extended than-function method [4], the exp -function method [5][6][7], sine-cosine method [8], the Inverse scattering transforms [9], the Jacobi elliptic function expansion [10], [11], the homogeneous balance method [12], the Homotopy perturbation methods [13], auxiliary equation method [14], the first integral method [15][16][17], the tanh-coth method [18], the Cole-Holf transformation method [19], the   '/ GG-expansion method [20][21][22], the improved   '/ GG -expansion method [23], the Enhance   '/ GG -expansion method [24] and so on. The improved…”