Abstract
The dynamics of solitons in birefringent optical fibers with Kerr law nonlinearity is studied in this paper, in presence of four-wave mixing terms in the governing model. There are three main types of exact one-soliton solutions retrieved for this dynamical system. They are bright, dark, and singular solitons. The ansatz approach is the integration tool for the governing coupled equations. Several constraint conditions naturally fall out during the course of integration of the corresponding coupled nonlinear partial differential equations.