This work devotes to explore abundant optical and other soliton solutions to fiber Bragg gratings with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are no doubt a technological spectacle that sustained balance between dispersion and nonlinear effects that leads to a stable transmission of solitons across intercontinental distances. Three reliable integration norms namely ([Formula: see text])-expansion function method, generalized tanh method and generalized Kudryashov method are engaging to devise optical dark, singular, combo, complex and periodic solutions. The reported solutions contain key applications in engineering and physics. These solutions define the wave performance of the governing models, actually. By the choice of suitable parametric values, the dynamics of the evaluated results are exemplified by sketching their 2D, 3D and contour profiles to understand the real phenomena for such sort of nonlinear models. The novelty of the gained outcomes is manifested by a detailed comparison with the results that already exist. The outcomes disclose that our schemes are very active reliable, concise, outspoken, appropriate, useful and skilled for attaining the exact solutions of such kind of problems which minimize the computational work and give it a wide range of applications.