Kinetic theory of parametric excitation of spin waves in the case of parallel pumping

Kinetic equations are constructed for normal and anomalous mean values of the type $f_{\mathrm p}=\langle a_{\mathrm p}^+a_{\mathrm p}\rangle$, $\sigma_{\mathrm p}=\langle a_{\mathrm p} a_{- \mathrm p}\rangle$ ($a_{\mathrm p}^+$, $a_{\mathrm p}$ are magnon operators) for ferromagnets under conditions of parallel pumping. Expressions are obtained for the generalized collision integrals in the equations for the functions $f_{\mathrm p}$ and $\sigma_{\mathrm p}$. Methods of obtaining solutions of the kinetic equations in a steady regime are discussed. An equation is formulated that describes the nonequilibrium states of the magnons in a region of the spectrum far from resonance.