  We derive coupled nonlinear Schr\"{o}dinger equation (CNLSE) for arbitrary
polarized light propagation in a single-mode fiber. We introduce a basis of
transverse eigen modes with the appropriate projecting hence solutions depend
on the waveguide geometry. Considering a weak nonlinearity which is connected
with Kerr effect, we give explicit expressions for nonlinear constants via
integrals of Bessel functions. We compare numerical results for the nonlinear
constant extracted from experimental observations of a soliton for the
nonlinear Schr\"{o}dinger equation (NLSE) (single-mode one). The method of
projecting we use allows a direct generalization to multi-mode fiber case.
