Influence of relaxation on nonlinear waves in crystals

A perturbation theory developed on the basis of the inverse scattering method is used to investigate the influence of transverse relaxation on a soliton of self-induced transparency in condensed media in the case of inhomogeneous broadening of the spectral line. It is shown that relaxation gives rise to excitation of a continuous spectrum of the scattering data of the auxiliary spectral problem and that this phenomenon leads to a change in the parameters of the nonlinear wave. Asymptotic expressions for the complex amplitude and energy and momentum of the extraordinary wave are determined. The parameters of a nonlinear wave propagating in a ruby crystal are calculated.