  We use a change of variables that turns the critical nonlinear Schroedinger
equation into the critical nonlinear Schroedinger equation with isotropic
harmonic potential, in any space dimension. This change of variables is
isometric on $L^2$, and bijective on some time intervals. Using the known
results for the critical nonlinear Schroedinger equation, this provides
information for the properties of Bose-Einstein condensate in space dimension
one and two. We discuss in particular the wave collapse phenomenon.
