Optical soliton perturbation with Fokas–Lenells equation via enhanced modified extended tanh-expansion approach

In this article, we establish novel solutions for the perturbed nonlinear Lenells equation, which is one of the model to investigate soliton dynamics through a polarization-preserving optical fiber, by using an enhanced modified extended tanh expansion method. Our aim is, not only gain various analytical optical soliton solutions of the investigated equation but also demonstrate the role of the investigated model’s parameter on soliton behavior, by selecting the different soliton shapes, which are bright and singular. In order to apply the proposed method, we first obtained the nonlinear ordinary differential form of the investigated equation with the help of complex wave transform. Then, by applying the method, we obtained the polynomial form and, accordingly, a system of linear equations. The solution of the linear system of equations gave different solution sets containing the values of the investigated model and the proposed method. After choosing the appropriate set from these sets and applying the solution functions and wave transformation provided by the method, we obtained the optical soliton solutions by providing the main equation. In order to support and better explain the obtained results, various graphic presentations were made by assigning some special values to the parameter values and explained in detail in the relevant sections. By applying the proposed method effectively, many analytical optical solutions of the model have been obtained and different soliton solutions have been obtained. Such as, bright, smooth V-shape, dark–bright in different amplitude, periodic singular, bright compacton like, composite dark–bright, periodic bright, breather like. More importantly, two different soliton types such as bright and singular were examined for the effect of model parameters on soliton behavior. The analysis shows that the model parameters have a significant effect on the soliton behavior and this effect might be different depending on the soliton types. Although the proposed method was applied to the investigated problem for the first time and different soliton types were obtained, the study differs from other studies in terms of examining the effect of model parameters on soliton behavior.