Study for obtaining the exact solutions for the propagation of pulses in optical fibers

In this study, the exact solutions for the propagation of pulses in optical fibers are obtained. Special values are given in the model used, and two nonlinear differential equations are obtained. Nonlinear equations are reduced to ordinary differential equations with the help of wave transformations. Then, the obtained differential equations are solved by two different methods, namely the modified simplest equation and the modified Kudryashov procedures. The solutions are given by hyperbolic, trigonometric and rational functions and the results are useful for optics, engineering and other related areas. Finally three-dimensional, contour and two-dimensional shapes are given for some solutions. These figures are important for understanding the motion of the wave. The given methods are applied to the equations for the first time. To the best of the authors’ knowledge, these results are new and have not been obtained in the literature. The results are useful for applied mathematics, physics and other related areas.