A non-integrable, variable coefficient nonlinear Schrodinger equation which governs the nonlinear
pulse propagation in an inhomogeneous medium is considered. The same equation is also applicable
to optical pulse propagation in averaged, dispersion-managed optical fiber systems, or fiber systems
with phase modulation and pulse compression. Multi-scale asymptotic techniques are employed to
establish the leading order approximation of a solitary wave. A direct numerical simulation shows
excellent agreement with the asymptotic solution. The interactions of two pulses are also studied.