Spectral representation of adiabatic interaction of cnoidal waves in an isotropic gyrotropic nonlinear medium

We analyse the evolution of the spectra of an approximate solution of the adiabatic interaction problem of two waves with orthogonal circular polarisations in an isotropic gyrotropic nonlinear medium with the second-order group velocity dispersion. It is shown that a gradual 'chaotisation' of the approximate solution for the amplitude of a rapidly changing wave is associated with its non-equidistant frequency spectrum.