Formation of shock waves in inhomogeneous active fibres

The formation dynamics of the shock wave of a pulse envelope is considered in fibres with the gain, dispersion, and nonlinearity distributed over the fibre length. It is shown that the wave-front steepness for inhomogeneous optical fibres can be strongly increased even when the local group-velocity dispersion substantially differs from zero if its average value (over the length of the shock-wave formation) is close to zero.