  An exactly soluble non-linear interaction Hamiltonian is proposed to study
fundamental properties of the entanglement dynamics for a coupled non-linear
oscillators. The time-evolved state is obtained analytically for initial
products of two coherent and two number states and relevant informations are
extracted from the dynamics of various quantities like subsystem linear and Von
Neumann entropies, quadrature mean values, variances and Q-functions. We
determined the re-coherence time scales and found among the interaction terms
present in the Hamiltonian the one responsible for the entanglement in both
cases. We identify the existence of two regimens for the entanglement dynamics
in the case of initially coherent states: the short time, phase spread regimen
where the entropy rises monotonically and the self-interference regimen where
the entropy oscillates and re-coherence phenomenon can be observed. We also
found that the break time from the first regimen to the second one becomes
longer, as well as the re-coherence and reversibility times, as the Planck's
constant becomes much smaller than a typical action in phase space.
