[en] The polariton dynamics in a microcavity in the parametric oscillator mode is studied when two pump polaritons turn into polaritons of signal and idler modes and vice versa. The pumping is performed by two laser pulses with close frequencies. Analytical solutions to a system of nonlinear differential equations are obtained. Periodic and aperiodic regimes of transformation of a pair of pump polaritons into polaritons of signal and idler modes, as well as the quiescent mode of the system, are obtained.

[en] We have studied the dynamics of polaritons in a microcavity in the parametric oscillator regime, when the pump is carried out by two laser pulses with close frequencies. Analytical solutions of a system of nonlinear differential equations with equal decay constants have been found.

[en] The dynamics of polaritons in a microcavity in the parametric oscillator mode, when two pump polaritons turn into the signal and idler polaritons and vice versa, has been studied. The pumping is carried out using two lasers with close frequencies. Analytical solutions of the system of nonlinear differential equations have been obtained. The periodic and aperiodic modes of the transformation of a pair of pump polaritons into signal and idler polaritons have been found.

[en] The dynamics of dipolariton states in a planar microcavity has been studied upon pumping of a state corresponding to the middle dipolariton branch. It has been shown that, under exact resonance conditions, both periodic and aperiodic regimes of conversion of pump dipolaritons to dipolaritons of idler and signal modes occur. The periodic regime of conversion of signal and idler dipolaritons without involving pump dipolaritons on the middle branch has also been analyzed.

[en] The results of investigation of the photodissociation dynamics of triatomic Bose-condensed ultracold molecules (trimers) with the formation of atoms and diatomic (dimer) pairs are presented. The interaction Hamiltonian is proposed, and a system of nonlinear equations is constructed that describes the evolution of atoms and molecules. Integrals of motion are obtained, and a nonlinear differential equation is derived for the time evolution of the atomic density with the use of these integrals. The solutions of this equation in various approximations imply that, depending on the initial conditions, different regimes of time evolution of the system are possible: periodic and aperiodic regimes.