Abstract
This paper studies the dynamics of slow light optical solitons from a mathematical point of view. It is mathematically proved that optical solitons, with a proper choice of time-dependent coefficients of dispersion and nonlinearity, can be made to slow down, and in the limiting case, to zero velocity. The types of nonlinearity that are studied in this paper are the Kerr law, power law, parabolic law, dual-power law and log law. Both bright and dark solitons are studied.