Hierarchy of Higher Dimensional Integrable System
Abstract
Integrable equations in (
1+1
) dimensions have their own higher order integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper we consider whether integrable equations in (
2+1
) dimensions have also the analogous hierarchies to those in (
1+1
) dimensions. Explicitly is discussed the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an ambiguity in the Painlevé test. Nevertheless, it may be concluded that the BS hierarchy is integrable.