n-Dimensional Bateman Equation and Painleve Analysis of Wave Equations

Abstract

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.