The Painleve Test of Higher Dimensional KdV Equation

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