In this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters

This paper applies a new approach including the trial equation based on the exponential function in order to find new traveling wave solutions to Zhiber-Shabat equation. By the using of this method, we obtain a new elliptic integral function solution. Also, this solution can be converted into Jacobi elliptic functions solution by a simple transformation.

In this study, the exact solutions of the Biswas-Arshed equation with the beta time derivative, which has an important role and physically means that it represents the pulse propagation in an optical fiber, nuclear, and particle physics, are obtained using the modified exponential function method. Exact solutions consisting of hyperbolic, trigonometric, rational trigonometric, and rational function solutions demonstrate the competence and relevance of the proposed method. In addition, the physical properties of the obtained exact solutions are shown by making graphical representations according to different parameter values. It is seen that the method used is an effective technique, since these solution functions obtained with all these cases have periodic function properties.

In this study, a new approach that assumes and is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-cosh-Gordon equations. Some new elliptic integral function solutions are respectively obtained by this method, and then these solutions are converted into the Jacobi elliptic function solutions. According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.

In this paper, we submit some new travelling wave solutions for the Vakhnenko--Parkes equation via the modified exponential function method. The obtained solutions include hyperbolic, exponential, trigonometric function solutions. Regarding these solutions, the 2D and 3D graphs and contour simulations are presented.