Bezvershenko I. Integrable models of quantum systems in external fields

We investigated the dynamical stabilization of spin system induced by a superposition of Rabi field and weak oscillating field. We proposed nonlinear modification of Rabi field for spin-1/2 and proposed the scheme for constructing the solutions. The resonance conditions are discussed. The representation of the spin states of Gaudin model in terms of generalized Laguerre polynomials was built. We investigated dynamics of Jaynes-Cummings model and introduced separated variables in Dicke model which lead to the generalized Jacobian. Dynamics of a 1D Bose-Einstein condensate induced by a sudden change of interaction parameter is studied and condition for splitting of initial soliton only into solitons is given.