Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)-Expansion Method

Abstract

We employ the (G′/G)-expansion method to seek exact traveling wave solutions of two nonlinear wave equations—Padé-II equation and Drinfel’d-Sokolov-Wilson (DSW) equation. As a result, hyperbolic function solution, trigonometric function solution, and rational solution with general parameters are obtained. The interesting thing is that the exact solitary wave solutions and new exact traveling wave solutions can be obtained when the special values of the parameters are taken. Comparing with other methods, the method used in this paper is very direct. The (G′/G)-expansion method presents wide applicability for handling nonlinear wave equations.

Equations of Nonlinear Waves in Thin Film Flows with Mass Sources and Surface Activity at the Moving Boundary

“…Unlike the statement of the problem in [2, 36,37], in the model proposed in this section, a source of liquid at the bottom will be taken into account. The goal of this section is to derive the governing propagation equation of nonlinear surface waves in moving thin films of perfect liquid in the presence of mass source of small intensity at the bottom.…”

“…in(36), i.e. increase in condensate flow rate, is related to the intensity of heat removal from the free surface of the film by the following relation…”

Solving Some Important Nonlinear Time-Fractional Evolution Equations by Using the (G’/G)-Expansion Method

“…More recently, the (G'/G)-expansion method (see [1][2][3][4][5][6][7][8][9][10]) has been proposed to obtain traveling wave solutions. This method is firstly proposed by Wang et al [10] for which the traveling wave solutions of the nonlinear evolution equations are obtained.…”

New Generalized Soliton Solutions for a (3+1)-Dimensional Equation

“…The research of the exact solutions for nonlinear equations plays a significant role in the investigation of nonlinear science. For nonlinear science, owing to containing more information and describing many natural phenomena, such as plasmas, gas dynamics, fluid mechanics, and elastic media, many nonlinear equations have been investigated [1][2][3][4][5][6][7][8][9][10]. Compared with the lower-dimensional nonlinear equations, the higher-dimensional nonlinear equations are more difficult to study because of the complex construction and multiple variables.…”