Peculiarities of periodic and aperiodic energy-exchange regimes in the cascade quasi-synchronous parametric frequency conversion

The domains of existence and peculiarities of exact analytic solutions of the problem of quasi-synchronous interaction of four plane collinear monochromatic waves - modes in a quadratically nonlinear medium during cascade frequency conversion are analysed. It is shown that the unusual types of multicomponent cnoidal and solitary soliton-like waves (of periodic and aperiodic energy-exchange regimes) are realised. Two of the four components of the latter are proportional to the real and imaginary parts of the well-known Lorentzian dependence, which is commonly used to describe the dispersion of contributions from resonance transitions to the complex permittivity in the case of homogeneous line broadening. (special issue devoted to the 80th birthday of s.a. akhmanov)