Nonlinear evolution of non-axisymmetric dynamical instability in a slender accretion torus

The nonlinear evolution of non-axisymmetric dynamical instability has been interpreted here within the framework of soliton theory. The dispersion relation of a two-dimensional slender accretion torus in the long wavelength incompressible limit is similar to that of the linearized KdV equation. We argue that the 'planet-like' solutions of nonlinear dynamical instability in the numerical simulations should be the soliton solutions of KdV equation. We also find that the vorticity of accretion disk is a non-conservation quantity due to the variation of density and entropy in the nonlinear evolution of dynamical instability. It is the cause of the redistribution of angular momentum during the instability.