New class of symmetries for self-gravitating hydrodynamics equations
  A method of calculating a new class of symmetries is presented for partial differential equations. The method give a new dynamical solution for an isothermal and cylindrically symmetric hydrodynamics equations under self-gravity. The solution describes a development of a gas cylinder from a motion-less state to states of expansion and oscillation. 
Souichi Murata and Kazuhiro Nozaki