Analytic Structure of the Landau-Ginzburg Equation in 2+1 Dimensions

Abstract

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.