Nonlinear magnetization dynamics in Bose-Einstein condensation of magnons

An equation for the dynamics of a Bose-Einstein condensate of magnons in a ferromagnetic film is presented, derived from quantum-mechanical theory. The main interactions affecting the evolution of the condensed state are considered. The transition from the equation for the annihilation operator of condensed magnons to an autonomous system of first-order differential equations describing their amplitude and phase is made. Phase trajectories of such a system were studied by constructing phase portraits and determining the stability of stationary points.