Instability of a light pulse in a nonlinear delayed-response scattering medium

The approximate method of smooth perturbations is used to analyze the instability of a light pulse traveling in a delayed-response medium with a scattering thermal nonlinearity. It is shown that maximally unstable perturbations grow in accordance with the law $\exp(1,16\surd\overline{S_0})$ where $S_0\thicksim I_0zt'$ is the total phase advance selfinduced over a distance $z$ in a time $t'$ from the beginning of a pulse and $I_0$ is the radiation flux. The instability is weaker than for an instantaneous-response focusing medium.