The paper deals with different formulations of mathematical models for the analysis of processes of resonance scattering and generation of plane wave packets on isotropic, nonmagnetic, linearly polarised media with a nonlinear, layered dielectric structure of cubic polarisability. For each formulation, sufficient conditions for the existence and, partially, uniqueness of the corresponding solution are derived.

resonance scattering, cubic polarisability, third harmonic generation (THG), frequency tripling, wave packets.