Analytical and numerical techniques are developed for the analysis of the solitary pulse propagation in a cylindrical media, where both the dispersion and diffraction management are known to exist. In the first part we treat the situation when there is no diffraction management by a simple analytical approach and show that it is possible to control both spatial and temporal width over one period of the dispersion map. An important out put of our analytical treatment is that we can predict the value of length of the second link and the amount of group velocity dispersion there if the initial conditions are given. Unfortunately since the spatial chirp can not be controlled, the treatment can not be repeated a second time. So for a long distance propagation a different treatment in needed. We then show that for long period of transmission, it is necessary to introduce diffraction management term, the best form turns out to be periodic function of the distanced travelled. The detailed variation of spatial and temporal width, chirp, and amplitude are explicitly given.