Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

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Abstract In this study, one of our main subjects is the examination of optical solitons of the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities via the modified F-expansion method. The other subject is also the analysis of the impacts of some parameters in the model on the soliton shape, which is examined for the first time in this study. According to the modified F-expansion method, we select the suitable transformation to gain the nonlinear ordinary differential equation for the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities in the first stage. Then, we get a system consisting of linear equations in polynomial form with the aid of the modified F-expansion method. Various solution sets consisting of the parameters of the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities are achieved. Inserting the selected sets and transformations into the serial form of the presented method and utilizing the solutions of the auxiliary equation in the presented method, the optical soliton solutions of the model are derived. Furthermore, varied optical soliton solutions, such as anti-kink, singular, and bright, are achieved, and 3D and 2D projections of the generated soliton solutions have been illustrated. The impact of some parameters on each soliton behavior has also been examined. It is found that these parameters have a significant impact on the soliton structure.