The soliton model of a ball lightning was further developed. It was suggested that a ball lightning is based on spherically symmetric nonlinear oscillations of charged particles in plasma – the analogue of a spatial Langmuir soliton. These oscillations were described in both classical and quantum approaches. It was found that the most intense plasma oscillations occur in the central regions of a ball lightning. It is suggested that bound states of radially oscillating charged particles with oppositely oriented spins – the analogue of Cooper pairs – can appear inside a ball lightning. This phenomenon, in its turn, can lead to a superconducting phase in a ball lightning. The idea of the superconductivity in a ball lightning was considered earlier. The possibility of the existence of a ball lightning with a composite core was also discussed in this model.