A superradiant pulse emitted by a sample of two-level atoms can be combined with superabsorption in order to increase the speed of the excitation interplay. We showcase this with two different experiments, first by subjecting the atomic sample to a competition between dissipation and amplification, the latter being a time-dependent multi-modal linear pumping; second, by coupling the atomic sample with a single mode of a high finesse cavity. The mean-field approximation was used in both cases. In the first, to solve the Schrödinger equation for the resulting time-dependent nonlinear Hamiltonian exactly we use the Lewis and Riesenfeld method. In the second case, we obtain a quantum master equation in the Lindblad form and solve it numerically. We observe that, in particular, the higher the number of atoms on the sample the higher will be the frequency of the interplay in comparison with that coming from the Jaynes-Cummings model. For a certain regime of parameters this system also leads to a superradiant laser, whose characteristics we discuss. These results show that many-particle effects can be further explored for the implementation of quantum information processes as well as for constructing of a superradiant laser. At last, we study non-Hermitian PT -symmetric bosonic nonautonomous Hamiltonians under linear and parametric amplifications. We present a generic approach to solve these Hamiltonians through the use of non-unitary similarity transformations. The choice for the metric associated with these transformations has a dramatic impact on the pseudo-Hermitian operators of the system.