dorsal/arxiv
View SchemaB\"acklund transformations for the second Painlev\'e hierarchy: a modified truncation approach
| Authors | Peter A. Clarkson, Nalini Joshi, Andrew Pickering |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9811014 |
| URL | https://arxiv.org/abs/solv-int/9811014 |
| DOI | 10.1088/0266-5611/15/1/019 |
Abstract
The second Painlev\'e hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well-known second Painlev\'e equation, P2. In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painlev\'e analysis to ordinary differential equations. We extend these techniques in order to derive auto-B\"acklund transformations for the second Painlev\'e hierarchy. We also derive a number of other B\"acklund transformations, including a B\"acklund transformation onto a hierarchy of P34 equations, and a little known B\"acklund transformation for P2 itself. We then use our results on B\"acklund transformations to obtain, for each member of the P2 hierarchy, a sequence of special integrals.
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"abstract": "The second Painlev\\\u0027e hierarchy is defined as the hierarchy of ordinary\ndifferential equations obtained by similarity reduction from the modified\nKorteweg-de Vries hierarchy. Its first member is the well-known second\nPainlev\\\u0027e equation, P2.\n In this paper we use this hierarchy in order to illustrate our application of\nthe truncation procedure in Painlev\\\u0027e analysis to ordinary differential\nequations. We extend these techniques in order to derive auto-B\\\"acklund\ntransformations for the second Painlev\\\u0027e hierarchy. We also derive a number of\nother B\\\"acklund transformations, including a B\\\"acklund transformation onto a\nhierarchy of P34 equations, and a little known B\\\"acklund transformation for P2\nitself.\n We then use our results on B\\\"acklund transformations to obtain, for each\nmember of the P2 hierarchy, a sequence of special integrals.",
"arxiv_id": "solv-int/9811014",
"authors": [
"Peter A. Clarkson",
"Nalini Joshi",
"Andrew Pickering"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0266-5611/15/1/019",
"title": "B\\\"acklund transformations for the second Painlev\\\u0027e hierarchy: a modified truncation approach",
"url": "https://arxiv.org/abs/solv-int/9811014"
},
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