The formation dynamics of a shock wave of the ultrashort pulse envelope in a medium with relaxing cubic nonlinearity

The effect of relaxation of nonlinearity on the formation of a shock wave of the intensity envelope of ultrashort laser pulses is studied on the basis of numerical analysis of the corresponding truncated wave equation. The relaxation of nonlinearity is shown to lead to the stabilisation of the envelope sharpening process, with the minimum width of the shock-wave front being limited by the relaxation time of nonlinearity. It is established that depending on the nonlinearity sign, the relaxation causes compression or spreading of the propagating pulse.