dorsal/arxiv
View SchemaSchlesinger Transformations for Linearisable Equations
| Authors | A. Ramani, B. Grammaticos, S. Lafortune |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9807003 |
| URL | https://arxiv.org/abs/solv-int/9807003 |
| Journal | Lett.Math.Phys. 46, 131-145 (1998). |
Abstract
We introduce the Schlesinger transformations of the Gambier equation. The latter can be written, in both the continuous and discrete cases, as a system of two coupled Riccati equations in cascade involving an integer parameter n. In the continuous case the parameter appears explicitly in the equation while in the discrete case it corresponds to the number of steps for singularity confinement. Two Schlesinger transformations are obtained relating the solutions for some value $n$ to that corresponding to either n+1 or n+2.
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"abstract": "We introduce the Schlesinger transformations of the Gambier equation. The\nlatter can be written, in both the continuous and discrete cases, as a system\nof two coupled Riccati equations in cascade involving an integer parameter n.\nIn the continuous case the parameter appears explicitly in the equation while\nin the discrete case it corresponds to the number of steps for singularity\nconfinement. Two Schlesinger transformations are obtained relating the\nsolutions for some value $n$ to that corresponding to either n+1 or n+2.",
"arxiv_id": "solv-int/9807003",
"authors": [
"A. Ramani",
"B. Grammaticos",
"S. Lafortune"
],
"categories": [
"solv-int",
"nlin.SI"
],
"journal_ref": "Lett.Math.Phys. 46, 131-145 (1998).",
"title": "Schlesinger Transformations for Linearisable Equations",
"url": "https://arxiv.org/abs/solv-int/9807003"
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