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

The effect of relaxation of nonlinearity on the formation of a shock wave o f the intensity envelope of ultrashort laser pulses is studied on the basis of numerical analysis of the corresponding truncated wave equation. The re laxation of nonlinearity is shown to lead to the stabilisation of the envel ope sharpening process, with the minimum width of the shock-wave front bein g limited by the relaxation time of nonlinearity, It is established that de pending on the nonlinearity sign, the relaxation causes compression or spre ading of the propagating pulse.