Abstract
This paper implements the trial equation approach to retrieve cubic-quartic optical solitons in fiber Bragg gratings with the aid of the trial equation methodology. Five forms of nonlinear refractive index structures are considered. They are the Kerr law, the parabolic law, the polynomial law, the quadratic-cubic law, and the parabolic nonlocal law. Dark and singular soliton solutions are recovered along with Jacobi's elliptic functions with an appropriate modulus of ellipticity.