Some effects of group-velocity dispersion on parametric interactions

Three-wave parametric interactions are studied in media exhibiting group-velocity dispersion. Under certain conditions these interactions may be described by the same equations that govern pulse propagation in a two-level resonant system. This analogy suggests the existence of steady-state pulse solutions in the three-wave parametric system. Such solutions are found, and are analogues of pi and two-pi pulses. The variety of solutions in the parametric system is greater than in the resonant case.