Abstract
The interaction of two pairs of wave packets propagating in a nondispersive and nondissipative medium with cubic non-linearity and two-photon transition is considered. It is assumed that the sum or difference of the carrying frequencies of waves belonging to the same pair is close to the frequency of this transition. It is shown that under some restrictions upon the group velocities of wave packets and the wave detuning the evolution equations may be integrated by the inverse scattering transform method. This method is used for studying the asymptotic behaviour of the fields in the framework of new integrable models. The nonsolitonic solution describing the decay of the unstable initial state of a system is investigated both analytically and numerically. Possible applications under specified experimental conditions are discussed.
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