Starting with the spinor representation of the electromagnetic field, we consider the propagation of a light beam along the Oz axis of a nonlinear medium. We first prove that for nonstationary processes in a one-dimensional space, the energy conservation takes the form of a conservation equation of kinematic waves. Then, using the method of characteristics, we discuss the self-steepening problem for initial value and boundary condition problems. We give the shock conditions and the shock velocity. The paper ends with a discus-sion of self-modulation.