Stability of nonlinear stationary waves in a cylinder of self-gravitating gas

In a self-gravitating gas, nonlinear periodic waves can propagate with an invariant profile. An expression is obtained for the stability of nonlinear stationary waves in a cylinder of self-gravitating gas. It is shown that the nonlinear waves are stable with respect to small perturbations with frequencies and wave numbers nearly equal to those of the waves. The present study may be relevant to the investigation of the role of density waves in the formation of star clusters