In this study, the dissipation problem of nonlinear pulse in mono mode optical fibers which is governed by the Fokas system (FS) is considered. The solutions of this system have an important role in comprehending the different wave structures in physical settings. Therefore, a new version of the trial equation method (NVTEM) is employed to present the new exact wave solutions of the FS. The advantage of the NVTEM is to use different root possibilities of a polynomial which shape the solutions of the related model. Primarily this system is converted to a nonlinear ordinary differential equation (NODE) via the traveling wave transform to apply the proposed method. Various exact wave solutions to the FS are obtained such as rational function, exponential function, hyperbolic function, and Jacobi elliptic function solutions. Thus, we have revealed solutions featly which are unlike the wave solutions previously found by other analytical methods. The present results depict the formation and development of such waves and their interactions. The exhibition of the solutions is given by 3D plots together with the corresponding 2D plots. The outcomes have shown that the proposed technique is abundant in achieving different wave solutions of many nonlinear differential equations in the field of optics.

In this study, the Lonngren-wave equation is considered to be analyzed for its wave solutions. To implement this purpose the modified exponential function method is used and ultimately new hyperbolic, trigonometric and rational forms of the exact solutions are obtained. Furthermore, it was tested whether these forms satisfy the Lonngren-wave equation or not and it was seen that they verify the equation. Besides this, the two and three dimensional graphics together with the contour and density plots are presented.

This work searches the new wave solutions of the time-fractional ion sound and Langmuir waves (ISLWs) equation and the time-fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation with the conformable derivative. The \(\left( m+\frac{1}{G^\prime }\right)\)-expansion method is employed for these models for the first time. Getting support from symbolic software, some new solutions are presented, which will be constructive for studies in the field of nonlinear physical phenomena. New wave solutions obtained by using the \(\left( m+\frac{1}{G^\prime }\right)\)-expansion method have applications in engineering, physics, and other scientific fields. The regarded method may provide a framework for the exact solutions of several evolution equations in applied sciences. Moreover, the graphical illustrations are also demonstrated to observe the dynamical behaviours of the solutions, which may benefit the development of new technologies.

In this study, the Landau-Ginzburg-Higgs (LGH) equation which has the physically important wave solutions is considered. This equation is discussed via modified exponential function method (MEFM) to describe superconductivity. Some new solutions are discovered in the form of rational, hyperbolic and trigonometric functions when compared with the ones taking part in the literature. The functions which are candidate to be the exact solutions of the nonlinear equation are tested by Mathematica program at the end of the steps of the method and it is observed that they satisfy the LGH equation. Additionally the 2-D and the 3-D graphs accompanying the density and contour plots are illustrated.

In this study a new version of the trial equation method (NVTEM) is employed to present the new exact wave solutions of the Fokas system which describes the propagation of nonlinear pulse in monomode optical fibers. Primarily this system is converted to a nonlinear ordinary differential equation (NODE) via the traveling wave transform to apply the proposed method. Various different exact wave solutions to the Fokas system are obtained such as rational function, exponential function, hyperbolic function and Jacobi elliptic function solutions. The exhibition of the solutions are given by 3D plots together with the corresponding 2D plots. The outcomes have shown that the proposed technique is abundant to achieve different wave solutions of many nonlinear differential equations in the field of optics.