dorsal/arxiv
View SchemaPeakons, R-Matrix and Toda-Lattice
| Authors | O. Ragnisco, M. Bruschi |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9509012 |
| URL | https://arxiv.org/abs/solv-int/9509012 |
| DOI | 10.1016/0378-4371(95)00438-6 |
Abstract
The integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the framework of the $r$-matrix approach, starting from its Lax representation. In the general case, the $r$-matrix is a dynamical one and has an interesting though complicated structure. However, for a particular choice of the relevant parameters in the hamiltonian (the one corresponding to the pure ``peakons" case), the $r$-matrix becomes essentially constant, and reduces to the one pertaining to the finite (non-periodic) Toda lattice. Intriguing consequences of such property are discussed and an integrable time discretisation is derived.
{
"annotation_id": "7f32b553-d10d-48e9-a6b1-5405dbffb925",
"date_created": "2026-03-02T18:02:51.407000Z",
"date_modified": "2026-03-02T18:02:51.407000Z",
"file_hash": "c0d0e7ffe7e167243ce6a5967e45aab5788099de71c5000745fe996de99837af",
"private": false,
"record": {
"abstract": "The integrability of a family of hamiltonian systems, describing in a\nparticular case the motionof N ``peakons\" (special solutions of the so-called\nCamassa-Holm equation) is established in the framework of the $r$-matrix\napproach, starting from its Lax representation. In the general case, the\n$r$-matrix is a dynamical one and has an interesting though complicated\nstructure. However, for a particular choice of the relevant parameters in the\nhamiltonian (the one corresponding to the pure ``peakons\" case), the $r$-matrix\nbecomes essentially constant, and reduces to the one pertaining to the finite\n(non-periodic) Toda lattice. Intriguing consequences of such property are\ndiscussed and an integrable time discretisation is derived.",
"arxiv_id": "solv-int/9509012",
"authors": [
"O. Ragnisco",
"M. Bruschi"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/0378-4371(95)00438-6",
"title": "Peakons, R-Matrix and Toda-Lattice",
"url": "https://arxiv.org/abs/solv-int/9509012"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f69a80b3-a89e-4ecb-8c50-f31ce1091040",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}