Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

In this study, we have focused on fnding soliton solutions of the cubic–quartic Fokas– Lenells equation, which models the nonlinear pulse transmission through optical fber, is a pretty new and updated model. The main motivation of this study is to produce new solutions with previously unused methods for data transmission models in fber optic cables together with the developing technology, which has been used very frequently today. We have used three diferent efcient analytical methods, namely, the Sinh–Gordon expansion method, enhanced modifed extended tanh expansion method and unifed Riccati equation expansion method. By modifying our proposed method and using it efectively, we have obtained much more optical solutions. We have supported the results with the 3D surface, 2D and contour plots of the soliton solutions, such as singular, periodic, periodic-singular, dark and M-shaped solitons. The originality of the method we propose is that it has never been used before. With the innovation of the method, we have obtained M-shaped solitons, which are very rarely obtainable in soliton waves. On the other hand, enhanced modifed extended tanh expansion method have provided us more extra solutions. As the last and most important part, in order to examine physical behaviors, we have investigated the efect of the coefcient of the fourth order dispersion parameter on wave propagation by presenting the graphical representation.