  We study the time evolution of two coupled quantum harmonic oscillators
interacting through nonlinear optomechanical-like Hamiltonians that include
cross-Kerr interactions. We employ techniques developed to decouple the
time-evolution operator and obtain the analytical solution for the time
evolution of the system. We apply these results to obtain explicit expressions
of a few quantities of interest. Our results do not require approximations and
therefore allow to study the nature and implications of the full nonlinearity
of the system. Potential applications and extensions to optomechanics are also
discussed.
