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A theoretical investigation is reported of the behavior of optical pulses under quasiresonant adiabatic tracking conditions. It is shown that dispersion of the group velocity and saturation of the populations of the resonant levels may give rise to soliton propagation of light. The exact solution for the envelope of a soliton is obtained for the first time subject to the saturation effect. Expressions are derived for the critical energy density in a soliton and for its duration. A study is made of the influence of the resonant saturation on the shape of a soliton envelope and its parameters. An analysis is reported of the behavior of light pulses of energies higher and lower than the critical value. It is shown that these pulses exhibit three types of quasisoliton propagation: weak, strong, and steady-state. The results for the pulses are generalized to two-dimensional light beams in a nonlinear waveguide.

An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.

An investigation is made of self-interaction of optical beams under one- and two-photon absorption conditions by solving nonlinear quasioptics equations using numberical techniques. An analysis is also made of self-focusing in the aberration-free approximation. The various self-interaction regimes are classified. A dependence of the threshold power on a factor characterizing the relationship between diffraction and saturation effects is obtained.

A theory is developed of transient excitation of polaritons by two light waves with frequencies differing by an amount corresponding to a phonon resonance region. A system of reduced equations is derived and it allows for the complex dispersion in the resonance region. Analytic and numerical methods are used to calculate the intensity profiles and energy characteristics of polariton radiation at and off a resonance.