Propagation of adiabatic ultrashort light pulses near a two-photon resonance

Nonlinear dispersion of the medium is taken into account in the derivation of the equations for self-consistent propagation of two adiabatic pulses when the sum of their frequencies is close to a two-photon resonance. Invariants describing the interaction of the two pulses are found. Analytic solutions are obtained for a special case. The nature of changes in the pulse profiles and their spectra during propagation are analysed. A critical propagation length at which a shock front appears in the pulse tails is considered as a function of the parameters of the problem.