An analytical treatment of the effect of axial inhomogeneity on femtosecond solitary waves near the zero dispersion point

A perturbed nonlinear Schrodinger equation, valid for femtosecond pulse propagation in axially inhomogeneous optical fibers near the zero dispersion point, is considered. It is found that for a weak axial nonuniformity, and under certain conditions, this equation can be treated analytically. Exact bright and dark solitary wave solutions are derived and their behavior in the presence of the inhomogeneity is analyzed. The nonuniformity induced time shift of the solitary waves is also obtained. The potential use of this parameter as a diagnostic tool for estimating characteristic parameters of the axial variations is discussed and its range of values is investigated.