dorsal/arxiv
View SchemaCanonical variables for multiphase solutions of the KP equation
| Authors | Bernard Deconinck |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9811006 |
| URL | https://arxiv.org/abs/solv-int/9811006 |
Abstract
The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical Hamiltonian system depending on a finite number of parameters is given for the description of each such solution. The Hamiltonian systems are completely integrable in the sense of Liouville. In effect, this provides a solution of the initial-value problem for the theta-function solutions. Some consequences of this approach are discussed.
{
"annotation_id": "82313fce-c9e5-4eda-a2de-556525ad7792",
"date_created": "2026-03-02T18:02:50.965000Z",
"date_modified": "2026-03-02T18:02:50.965000Z",
"file_hash": "d98b89940c75e3563f1524522203d588883176a330e6447192c48589e608e475",
"private": false,
"record": {
"abstract": "The KP equation has a large family of quasiperiodic multiphase solutions.\nThese solutions can be expressed in terms of Riemann-theta functions. In this\npaper, a finite-dimensional canonical Hamiltonian system depending on a finite\nnumber of parameters is given for the description of each such solution. The\nHamiltonian systems are completely integrable in the sense of Liouville. In\neffect, this provides a solution of the initial-value problem for the\ntheta-function solutions. Some consequences of this approach are discussed.",
"arxiv_id": "solv-int/9811006",
"authors": [
"Bernard Deconinck"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Canonical variables for multiphase solutions of the KP equation",
"url": "https://arxiv.org/abs/solv-int/9811006"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "330c0e18-83ef-419e-9957-155182b12a48",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}