dorsal/arxiv
View SchemaMappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
| Authors | Pilar R. Gordoa, Nalini Joshi, Andrew Pickering |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904023 |
| URL | https://arxiv.org/abs/solv-int/9904023 |
| DOI | 10.1088/0951-7715/12/4/313 |
Abstract
The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.
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"abstract": "The truncation method is a collective name for techniques that arise from\ntruncating a Laurent series expansion (with leading term) of generic solutions\nof nonlinear partial differential equations (PDEs). Despite its utility in\nfinding Backlund transformations and other remarkable properties of integrable\nPDEs, it has not been generally extended to ordinary differential equations\n(ODEs). Here we give a new general method that provides such an extension and\nshow how to apply it to the classical nonlinear ODEs called the Painleve\nequations. Our main new idea is to consider mappings that preserve the\nlocations of a natural subset of the movable poles admitted by the equation. In\nthis way we are able to recover all known fundamental Backlund transformations\nfor the equations considered. We are also able to derive Backlund\ntransformations onto other ODEs in the Painleve classification.",
"arxiv_id": "solv-int/9904023",
"authors": [
"Pilar R. Gordoa",
"Nalini Joshi",
"Andrew Pickering"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0951-7715/12/4/313",
"title": "Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations",
"url": "https://arxiv.org/abs/solv-int/9904023"
},
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