Non linear stability of slender accretion disks by bifurcation method

The nonlinear evolution of a constant angular momentum accretion disk subject to Papaloizou and Pringle (1984; hereafter PP) instability is investigated. The analysis is performed on an inviscid incompressible two-dimensional model using a formalism suitable for Hamiltonian systems. Only the most unstable modes are taken into account. It is found that relevant nonlinear terms have a stabilizing influence on the system. This supports recent numerical experiments showing a transition towards a quasi-stable planet configuration. The extension of the method to fat disk instabilities, more relevant to AGN disks, is discussed.