Conformal symmetry of the coupled Chern-Simons and gauged nonlinear   Schr\"odinger equations
  The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schr\"odinger equations in the plane is derived in a non-relativistic Kaluza-Klein framework. 
C. Duval, P.A. Horvathy and L. Palla