The modified simple equation (MSE) method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in engineering and mathematical physics. In this study, we bring to bear the MSE method to look for the exact solutions via the Tzitzeica–Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations involving parameters. When the parameters receive special values, solitary wave solutions are derived from the exact solutions. By means of this scheme, we found some fresh traveling wave solutions of the above mentioned equations

The modified simple equation (MSE) method is promising for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this letter, we investigate solutions of the (2+1)-dimensional Zoomeron equation and the (2+1)-dimensional Burgers equation by using the MSE method and the Exp-function method. The competence of the methods for constructing exact solutions has been established

The purpose of this article is to present an analytical method, namely the improvedF-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

In this paper, the modified simple equation (MSE) method is implemented to find the exact solutions for the nonlinear Drinfel’d–Sokolov–Wilson (DSW) equation and the modified Benjamin–Bona–Mahony (mBBM) equations. The efficiency of this method for constructing these exact solutions has been demonstrated. It is shown that the MSE method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this technique reduces the large volume of calculations

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. Mathematics subject classification 35C07; 35C08; 35P99

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions–hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg