Weak damping slow modes of oriented nonlinear oscillations in liquid crystalls in unstabilizing magnetic fields

Nonlinear inertial torsion oscillations of the structure of nematic liquid crystall in unstabilizing magnetic field have low frequency modes possessing the anomaly weak damping. The corresponding solution of the sine-Gordone type equation to the account for viscous rotating friction describes the transitions via the potential barrier between two equillibrium states. We show that when the oscillation amplitude is large enough to overcome the barrier, the damping time for the period of oscillation diverges logarithmically.