Radial solitary waves in periodic variable stars
  It is shown that the oscillations of brightness in classical Cepheids and other 'pulsating' variable stars are caused rather by the passing of radial solitary waves through the photosphere of a star, than by pulsations of a star. Radial solitary waves also determine the oscillations of brightness in some other types of periodic variable stars ordinary not considered as pulsating stars. 
Fedor V.Prigara