n-Dimensional Bateman Equation and Painleve Analysis of Wave Equations

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.