The Painlevé Test of Higher Dimensional KdV Equation

Abstract

We argue the integrability of the generalized KdV(GKdV) equation using the Painlevé test. For $d(\le 2)$ dimensional space, GKdV equation passes the Painlevé test but does not for $d\ge 3$ dimensional space. We also apply the Ablowitz-Ramani-Segur's conjecture to the GKdV equation in order to complement the Painlevé test.

arXiv comment7 pages, LaTeX