  In the Painleve analysis of nonintegrable partial differential equations one
obtains differential constraints describing the movable singularity manifold.
We show, for a class of n-dimensional wave equations, that these constraints
have a general structure which is related to the $n$-dimensional Bateman
equation. In particular, we derive the exact expressions of the singularity
manifold constraints for the n-dimensional sine-Gordon -, Liouville -,
Mikhailov -, and double sine-Gordon equation, as well as two 2-dimensional
polynomial field theory equations, and prove that their singularity manifold
conditions are satisfied by the n-dimensional Bateman equation. Finally we give
some examples.
