This paper obtains the 1-soliton solution of birefringent fibers, with Kerr law nonlinearity, in presence of perturbation terms. The perturbation terms that are studied are the inter-modal dispersion, third order dispersion, self-steepening term and nonlinear dispersion. Bath bright and dark soliton solutions are considered. There are several constraint conditions that fall out during the course of derivation of the soliton solutions. The numerical simulations are also provided.