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.

PT Journal Article
TI Spin-wave turbulence beyond the parametric excitation threshold
AU Zakharov V E
FAU Zakharov VE
AU L’vov V S
FAU L’vov VS
AU Starobinets S S
FAU Starobinets SS
DP 10 Jun, 1975
TA Phys. Usp.
VI 18
IP 6
PG 896-919
RX 10.1070/PU1975v017n06ABEH004404
URL https://ufn.ru/en/articles/1975/6/q/
SO Phys. Usp. 1975 Jun 10;18(6):896-919