Characteristic modes of vibration of Q-balls

In this report, based on [1], we study analytically small perturbations of classically stable Q-balls in 3+1 dimensions. Models with flat and polynomial potentials are considered. We find that large Q-balls in the model with the flat potential possess soft modes. We also find a specific mode for Q-balls near the stability bound, which is related to the decay mode of Q-clouds. For these modes, the perturbation theory is applicable with respect to the relative frequency of an excitation.