Abstract
The current work addresses cubic-quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic-quartic version of the perturbed Fokas-Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude-width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist.