Detailed calculations of the properties of soliton propagation related to director motion in nematic liquid crystals under shear flow (including the presence of external magnetic or electric field) are given for the first time. Analytic soliton solutions are obtained when wave velocity is large. The properties of soliton solution, the energy of soliton and the interference patterns of polarized (monochromatic or white) light caused by the movement of such solitons are calculated and discussed. Eecent experiments of Refs. [12] and [13] are analysed and the dark lines observed in liquid crystal MBBA are shown to correspond to the type A soliton presented in this paper.