dorsal/arxiv
View SchemaDiscrete and Continuous Linearizable Equations
| Authors | S. Lafortune, B. Grammaticos, A. Ramani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9812024 |
| URL | https://arxiv.org/abs/solv-int/9812024 |
| DOI | 10.1016/S0378-4371(99)00026-6 |
| Journal | Physica A, 268, 129-141 (1999) |
Abstract
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one and reduce the system to a single differential equation. This equation is of the form of those singled-out by Painlev\'e in his quest for integrable forms. In the discrete case, we extend previous results of ours showing that, again by elimination of variables, the general projective system can be written as a mapping for a single variable. We show that this mapping is a member of the family of multilinear systems (which is not integrable in general). The continuous limit of multilinear mappings is also discussed.
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"abstract": "We study the projective systems in both continuous and discrete settings.\nThese systems are linearizable by construction and thus, obviously, integrable.\nWe show that in the continuous case it is possible to eliminate all variables\nbut one and reduce the system to a single differential equation. This equation\nis of the form of those singled-out by Painlev\\\u0027e in his quest for integrable\nforms. In the discrete case, we extend previous results of ours showing that,\nagain by elimination of variables, the general projective system can be written\nas a mapping for a single variable. We show that this mapping is a member of\nthe family of multilinear systems (which is not integrable in general). The\ncontinuous limit of multilinear mappings is also discussed.",
"arxiv_id": "solv-int/9812024",
"authors": [
"S. Lafortune",
"B. Grammaticos",
"A. Ramani"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/S0378-4371(99)00026-6",
"journal_ref": "Physica A, 268, 129-141 (1999)",
"title": "Discrete and Continuous Linearizable Equations",
"url": "https://arxiv.org/abs/solv-int/9812024"
},
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