Results are given on the investigation of optical bistability and multistability phenomena both, in the exciton range of the spectrum due to exciton-photon and exciton+xciton interactions and in the range of two-photon generation of the biexcitons (excitonic molecules). For each case the steady-state equations are obtained. npeACTaBJIeHbI pe3yJlbTaTbI ZICCJleAOBaHHII IIBJIeHMFi OllTM'leCKOfi 6MCTa6HJlbHOCTH U MYJIbTHCTa6HJl@HOCTEi KBK B 3KCUTOHHOa o 6 n a c~~ ClleKTpa C YYeTOM 3IECEITOH-@OTOHHO~O U3KCHTOH-3KCUTOAHO~O B3aHMOnefiCTBHfi, TBK U B 06nac~u nByX@OTOHHOrO B036yXneHUfi 6kl3HCEiTOHOB @OTOHaMH ABYX pa3JlllYHbIX HMIIynbCOB. nOJlyYeHhl YpaBHeHHFi COCTORHElH n m Kamnoro ~3 cnysaeB.

The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum has already been studied in a set of papers /1 to 5/. The major results concerning the coherent nonlinear propagation of ultra-short and short pulses of the resonant laser radiation exciting excitons in crystals a r e reflected in them.The interaction in a system of excitons of high density and the effect of dipole momentum saturation for the transition from the ground state of the crystal to the exciton one a r e the nonlinear t e r m s of the Hamiltonian. Their joint action leads to the stabilization of the wave packet envelopes and the soliton formation.The magnitude of the exciton translational mass and the spatial dispersion effects play a secondary role in the considered range of the spectrum and will not b e taken into account. This is connected with the fact that the polariton effect, i. e. the mixing of the free exciton and photon bands plays the main role. The spectrum mixing leads to the existence of lower and upper polariton branches, which have small negative values of effective masses correspondingly. This circumstance favours the formation of polariton solitons, the linear dimensions of which in the direction of travelling a r e greater than the light wavelength.The conditions of light travelling through the crystal-vacuum interface were not considered in the previous works, though they a r e of interest for any experiment.We want to determine the necessary parameters of the incident l a s e r ultrashort pulses. They must have such a time width, power, and envelope that after the penetration into the crystal they could travel at once as a solitary wave without distortion. For that purpose we employed the Maxwell-Fresnel boundary conditions. 1 ) Akademicheskaya 5, 2 77028 Kishinev, USSR.

The energy flux density of the incident light upon the crystal surface and the form of the wave packet envelope with frequencies lying in the exciton range of the spectrum, are determined. They must be of such a nature that after the penetration into the semi-infinite crystal, the laser pulse can travel at once as a solitary wave without any transient stage. I n the case considered the effect of the dipole momentum saturation (DMS) for the transition from the ground state of tho crystal t o that of the exciton is the main nonlinearity. The Maxwell-Bresnel boundary conditions are used on the interface between the vacuum and the crystal.Die EnergiefluIjdichte des einfallenden Lichtes auf die Kristalloberfliiche und die Form der Einhiillenden des Wellenpakets bei Frequenzen im Exzitonenbereich des Xpektrums werden bestimmt. Sie miissen von solcher Art sein, daIj nach dem Eintritt in den halbunendlichen Kristall, der Laserimpuls im ganzen als Solitarwelle ohne jeden Ubergangszustand laufen kann. I m vorliegenden Fall ergibt der EinfluIj der Dipol-Impulssattigung (DMX) fur den ubergang vom Grundzustand des Kristalls zum Exziton die Hauptnichtlinearitat. Die Maxwell-Fresnel-Randbedingungen werden an der Grenzflache ewischen Vakuum und Kristall benutzt.

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A phenomenological theory of t.he nonlinear multistable light transmission by a semiconductor slab is presented taking into account the variation of the amplitude reflection coefficients of the interfaces versus the level of the excitation. It is shown, that the reflection c0efficient.s of the front and back end faces of the slab are different. In the dispersive limit a generalized Airy formula for the multistable transmission is found.