  We discuss collisionless kinetic equations describing the non-equilibrium
dynamics of magnons in a ferromagnet exposed to an oscillating microwave field.
Previously, this problem has been treated within the so-called "S-theory" where
the collision integral in the kinetic equation for the magnon distribution is
either neglected or taken into account phenomenologically via an effective
relaxation time. However, the possibility of magnon condensation has not been
included in S-theory. Moreover, the momentum integrations appearing in the
magnon self-energies are usually decoupled by retaining only the term where the
loop momentum is equal to the external momentum. In this work we critically
examine the accuracy of these approximations and develop the proper extensions
of S-theory. We show that these extensions can significantly modify the time
evolution of the magnon distribution.
