Optical solitons in fibre Bragg gratings with third- and fourth-order dispersive reflectivities

. For the first time in the field of nonlinear optics, we address cubic–quartic solitons appearing in the fibre Bragg gratings with dispersive reflectivity for four different cases of nonlinear refractive-index structures. A complete spectrum of single solitons, together with some straddled solitons, emerges from the integration scheme adopted by us, which is the approach of sine–Gordon equation. within this integration scheme, which is discussed in this work. The details will be sketched after a brief introduction into our model.