Group-invariant Solutions of the 2+1-dimensional Cubic Schr\"odinger   Equation
  Lie point symmetries of the 2+1-dimensional cubic Schr\"odinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable they typically can belong to the class of Painlev\'e type equations. 
C. Ozemir and F. Gungor