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Hierarchy of Higher Dimensional Integrable System

Yu Song-Ju·Kouichi Toda·Takeshi Fukuyama
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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.

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Yu Song-Ju, Kouichi Toda, Takeshi Fukuyama. 1998-02-03. Hierarchy of Higher Dimensional Integrable System. https://arxiv.org/abs/solv-int/9802005

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