Weakly nonlinear theory of the Jeans instability in disk galaxies of stars

The reaction of collective oscillations excited in the interaction between aperiodically growing Jeans-type gravity perturbations and stars of a rapidly rotating disk of flat galaxies is considered. An equation is derived which describes the change in the main body of equilibrium distribution of stars in the framework of the nonresonant weakly nonlinear theory. Certain applications of the theory to the problem of relaxation of the Milky Way at radii where two-body relaxation is not effective are explored. The theory, as applied to the Solar neighborhood, accounts for observed features, such as the shape for the velocity ellipsoid of stars and the increase in star random velocities with age.