Nonlinear instability of a gravitating disk

The nonlinear growth regime of perturbations is analyzed up to the fifth order in their amplitude for a rotating, gravitating model gaseous disk. In the isothermal case (adiabatic index γ = 1) the breakup instability predicted by Mikhailovskii et al. will be stabilized for perturbations of finite amplitude, but in the case of a monatomic gas (γ = 5/3) their conclusion that breakup instability will occur is confirmed (if one adopts the model of a low-mass gaseous disk embedded in a massive disk of stars). The series in powers of the perturbation amplitude given by the theory may possibly be asymptotic