Nonlinear stage of gravitational instability in flat gaseous systems

Evolution of finite amplitude waves in flat gaseous gravitationing systems is studied. Small oscillations of rotating flat gaseous layer with γ adiabate index are considered. On the basis of hydrodynamics equations and of Poisson equation (by numerical methods) built up is the nonlinear theory of equilibrium model oscillations. Found are limitations on physical states of gas at which a high growth of density disturbances is possible. A critical value of adiabate index γsub(c) approximately 1.404 is determined for rotating gaseous layer. It is shown that density disturbances may grow up to large values only at considerably low γ < γsub(c)