Autoresonance excitation of a breather in weak ferromagnetics

A mathematical model of the magnetodynamics of a weak ferromagnetic in an external magnetic field with variable frequency is studied. Conditions for the appearance of autoresonance are found under which the amplitude of the local magnetic inhomogeneities is considerably increased. Mathematically, the problem is to analyze the solutions to the sine-Gordon equation subject to a specific nonautonomous perturbation. For the perturbed equation, asymptotic solutions in the form of a breather with a slowly varying amplitude and a phase shift are constructed. The solutions whose amplitude increases with time from small values to quantities of order one are associated with the autoresonance phenomenon.