dorsal/arxiv
View SchemaHierarchy of Higher Dimensional Integrable System
| Authors | Yu Song-Ju, Kouichi Toda, Takeshi Fukuyama |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9802005 |
| URL | https://arxiv.org/abs/solv-int/9802005 |
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 Painlev\'e test. Nevertheless, it may be concluded that the BS hierarchy is integrable.
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"abstract": "Integrable equations in ($1 + 1$) dimensions have their own higher order\nintegrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper\nwe consider whether integrable equations in ($2 + 1$) dimensions have also the\nanalogous hierarchies to those in ($1 + 1$) dimensions. Explicitly is discussed\nthe Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an\nambiguity in the Painlev\\\u0027e test. Nevertheless, it may be concluded that the BS\nhierarchy is integrable.",
"arxiv_id": "solv-int/9802005",
"authors": [
"Yu Song-Ju",
"Kouichi Toda",
"Takeshi Fukuyama"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Hierarchy of Higher Dimensional Integrable System",
"url": "https://arxiv.org/abs/solv-int/9802005"
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