Painlevé Test

A partial differential equation has the Painlevé property when the solution of the partial differential equation considered in the complex domain is single-valued about the movable, singularity manifold. One requires that the solution be a single-valued functional of the data, i.e., arbitrary functions. To prove that a partial differential equation has the Painlevé property one expands a solution about a movable singular manifold ø(z₁, …, z_n) = 0…