In this work, the nonlinear Schrödinger’s equation is studied for birefringent fibers incorporating four-wave mixing. The improved tanϕ(ξ)2-expansion, first integral, and G′G2-expansion methods are used to extract a novel class of optical solitons in the quadratic-cubic nonlinear medium. The extracted solutions are dark, periodic, singular, and dark-singular, along with other soliton solutions. These solutions are listed with their respective existence criteria. The recommended computational methods here are uncomplicated, outspoken, and consistent and minimize the computational work size, which give it a wide range of applicability. A detailed comparison with the results that already exist is also presented.
