  In this paper it is shown that deferentially rotating disks that are in the
presence of weak axial magnetic field are prone to a new nonlinear explosive
instability. The latter occurs due to the near-resonance three-wave
interactions of a magnetorotational instability with stable Alfven-Coriolis and
magnetosonic modes. The dynamical equations that govern the temporal evolution
of the amplitudes of the three interacting modes are derived. Numerical
solutions of the dynamical equations indicate that small frequency mismatch
gives rise to two types of behavior: 1. explosive instability which leads to
infinite values of the three amplitudes within a finite time, and 2. bounded
irregular oscillations of all three amplitudes. Asymptotic solutions of the
dynamical equations are obtained for the explosive instability regimes and are
shown to match the numerical solutions near the explosion time.
