dorsal/arxiv
View SchemaThe Gambier Mapping, Revisited
| Authors | B. Grammaticos, A. Ramani, S. Lafortune |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9804011 |
| URL | https://arxiv.org/abs/solv-int/9804011 |
| DOI | 10.1016/S0378-4371(97)00675-4 |
| Journal | Physica A 253, 260-270 (1998) |
Abstract
We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable through linearisation. We then introduce the general discrete form of this equation, the Gambier mapping, and present conditions for its integrability. Finally, we obtain the reductions of the Gambier mapping, identify their integrable forms and compute their continuous limits.
{
"annotation_id": "c6d55f45-653a-4576-bd70-4fec994fb6cf",
"date_created": "2026-03-02T18:02:50.706000Z",
"date_modified": "2026-03-02T18:02:50.706000Z",
"file_hash": "a9f9c2825fbd84f02b8bf621b127e9b7d30bd040574a9a736a25958474213274",
"private": false,
"record": {
"abstract": "We examine critically the Gambier equation and show that it is the generic\nlinearisable equation containing, as reductions, all the second-order equations\nwhich are integrable through linearisation. We then introduce the general\ndiscrete form of this equation, the Gambier mapping, and present conditions for\nits integrability. Finally, we obtain the reductions of the Gambier mapping,\nidentify their integrable forms and compute their continuous limits.",
"arxiv_id": "solv-int/9804011",
"authors": [
"B. Grammaticos",
"A. Ramani",
"S. Lafortune"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/S0378-4371(97)00675-4",
"journal_ref": "Physica A 253, 260-270 (1998)",
"title": "The Gambier Mapping, Revisited",
"url": "https://arxiv.org/abs/solv-int/9804011"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "feb06744-da9a-4ddb-a2ff-620dfed0d8d5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}