  In this paper, two methods are employed to investigate for which values of
the parameters, if any, the two-dimensional real Landau-Ginzburg equation
possesses the Painleve property. For an ordinary differential equation to have
the Painleve property all of its solutions must be meromorphic but for partial
differential equations there are two inequivalent definitions, one a direct
investigation of a Laurent series expansion and the other indirect and relying
on a knowledge of the continuous symmetry group of the equation. We check both
methods for the Landau-Ginzburg equation in 2+1 dimensions and each one yields
that this equation does not possess the Painleve property for any values of the
parameters.
