We consider the soliton-like pulse propagation through birefringent optical fibers with fourth order dispersion, where the pulse dynamics is governed by coupled nonlinear Schrödinger (CNLS) type equations. In order to analyze the state of polarization of a soliton like pulse, we construct the integro-differential equations from the CNLSE using the Stokes parameter formalism. After constructing the suitable equations of motion, we also discuss the rotation of the Stokes vector on the Poincaré sphere.