Nonlinear Density Waves in Galaxies

This paper concerns the dynamics of a nonlinear density wave which is stationary in the sense that it possesses a time-independent structure in a uniformly rotating frame of reference. Waves which prove to be the nonlinear analogues of the waves described by the linear theory of Lin and Shu are investigated in detail. A condition for the occurrence of such waves is that the galaxy must be composed of subsystems of two well-defined types which correspond to the stellar populations of the Galaxy and of similar galaxies. A corollary of this condition is that the spiral pattern of a wave is relatively more open the larger the fraction of the mass of the galaxy in subsystems of the type belonging to Population I.