dorsal/arxiv
View SchemaOn a Schwarzian PDE associated with the KdV Hierarchy
| Authors | Frank Nijhoff, Andrew Hone, Nalini Joshi |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9909026 |
| URL | https://arxiv.org/abs/solv-int/9909026 |
| DOI | 10.1016/S0375-9601(00)00063-3 |
Abstract
We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered as the generating equation for the entire hierarchy of Schwarzian KdV equations. We present its Lax pair, establish its connection with the SKdV hierarchy, its Miura relations to similar generating PDEs for the modified and regular KdV hierarchies and its Lagrangian structure. Finally we demonstrate that its similarity reductions lead to the {\it full} Painlev\'e VI equation, i.e. with four arbitary parameters.
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"abstract": "We present a novel integrable non-autonomous partial differential equation of\nthe Schwarzian type, i.e. invariant under M\\\"obius transformations, that is\nrelated to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered\nas the generating equation for the entire hierarchy of Schwarzian KdV\nequations. We present its Lax pair, establish its connection with the SKdV\nhierarchy, its Miura relations to similar generating PDEs for the modified and\nregular KdV hierarchies and its Lagrangian structure. Finally we demonstrate\nthat its similarity reductions lead to the {\\it full} Painlev\\\u0027e VI equation,\ni.e. with four arbitary parameters.",
"arxiv_id": "solv-int/9909026",
"authors": [
"Frank Nijhoff",
"Andrew Hone",
"Nalini Joshi"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/S0375-9601(00)00063-3",
"title": "On a Schwarzian PDE associated with the KdV Hierarchy",
"url": "https://arxiv.org/abs/solv-int/9909026"
},
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