Kinetic description of collective oscillations in a system of parametric spin waves II. Inhomogeneous collective modes

On the basis of the linearized kinetic equations obtained in Part I, spatially inhomogeneous collective oscillations in a system of parametric spin waves of a ferromagnet are considered. It is shown that the spectrum $\Omega_m(\varkappa)$ of such oscillations depends on the relationship between the wave number $\varkappa$ of the oscillations and the spreading $\Delta k$ of the packet of parametric waves in the $\mathbf k$ space. An investigation is made into the behavior of the spectrum $\Omega_0(\varkappa)$ of an inhomogeneous zero-order mode near the stability boundaries of the isotropic stationary state and the anisotropic stationary states. Criteria of stability of the stationary states with respect to excitation of the inhomogeneous zero-order mode in the longwavelength ($\varkappa\ll\Delta k$) and short-wavelength ($\varkappa\gg\Delta k$) regions of the spectrum are obtained. For higher modes with $m\not=0$, the spectrum of longitudinal ($\varkappa\Vert\mathbf M_0$) long-wave and short-wave collective oscillations is found.