Spin-wave turbulence beyond the parametric excitation threshold

The nonlinear stage of the parametric excitation of spin waves in ferromagnetic dielectrics is reviewed. The main nonlinear mechanism which limits the amplitude of the exponentially growing waves is the “pairing” of waves with equal and opposite wave vectors, which leads to the violation of phase relationships. This effect is described in terms of a Hamiltonian which is diagonal in the wave pairs; The corresponding approximation is called the $S$ theory. Within the framework of this theory, the distribution of the excited waves in $\mathbf{k}$ space is singular: the waves lie on individual lines or points. Consequences of the $S$ theory and their experimental verification are discussed in detail. Collective oscillations of a spin-wave system and the origin of the observed self-modulation of their amplitude are also considered.