The dynamics of solitons in birefringent optical fibers with weak nonlocal 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. The approach is based in the modified sub-equation extended method for the generalized hyperbolic and trigonometric functions for constructing new exact solutions of the governing coupled equations in birefringent optical fibers. Several constraint conditions naturally fall out during the course of integration of the corresponding coupled nonlinear partial differential equations.
