The Painlev\'e Test of Higher Dimensional KdV Equation

/ Authors

/ Abstract

We argue the integrability of the generalized KdV(GKdV) equation using the Painlev´e test. For d ( ≤ 2) dimensional space, GKdV equation passes the Painlev´e test but does not for d ≥ 3 dimensional space. We also apply the Ablowitz-Ramani-Segur’s conjecture to the GKdV equation in order to complement the Painlev´e test.

The Painlev\'e Test of Higher Dimensional KdV Equation

/ Authors

Yu.Song-Ju, T.Fukuyama

/ Abstract

We argue the integrability of the generalized KdV(GKdV) equation using the Painlev´e test. For d ( ≤ 2) dimensional space, GKdV equation passes the Painlev´e test but does not for d ≥ 3 dimensional space. We also apply the Ablowitz-Ramani-Segur’s conjecture to the GKdV equation in order to complement the Painlev´e test.