On the self-induced transparency effect of the three-wave resonance process

The self-induced transparency effect of the three-wave resonance is studied by the inverse scattering method. By transforming to the characteristic coordinates of the background wave, the inverse-scattering theory becomes greatly simplified. With the presence of a constant background wave, the three-wave process is dispersive, and the solitons and continuum behave in a different way from those of spatially bounded wavepackets. The continuum decays away, depositing energy to the background. The solitons have velocities which are amplitude dependent.