Singularity Analysis of Spherical Kadomtsev–Petviashvili Equation

Abstract

The (2+1)-dimensional spherical Kadomtsev–Petviashvili (SKP) equation of J.-K. Xue [Phys. Lett. A 314 (2003) 479] fails the Painlevé test for integrability at the highest resonance, where a nontrivial compatibility condition for recursion relations appears. This compatibility condition, however, is sufficiently weak and thus allows the SKP equation to possess an integrable (1+1)-dimensional reduction, which is found by the method of truncated singular expansion.