Hierarchy of Higher Dimensional Integrable System

Song-Ju, Yu; Toda, Kouichi; Fukuyama, Takeshi

Hierarchy of Higher Dimensional Integrable System

Authors

Song-Ju, Yu

Toda, Kouichi

Fukuyama, Takeshi

Description

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.
10 pages, uses ioplppt.sty