This paper addresses soliton propagation through optical fibers by the aid of Biswas–Milovic equation that serves as a generalized version of the usual nonlinear Schrodinger’s equation. Several integration schemes are implemented to secure solitons and other solutions to the model. There are two types of nonlinear media that are studied. They are power law and dual-power law so that Kerr law and parabolic law emerge as special cases to these two laws.