dorsal/arxiv
View SchemaN-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation
| Authors | S. J. Yu, K. Toda, T. Fukuyama |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9803012 |
| URL | https://arxiv.org/abs/solv-int/9803012 |
| DOI | 10.1088/0305-4470/31/50/013 |
Abstract
We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, $\phi_{xt} + \phi_{xxxz}/4 + \phi_x \phi_{xz} + \phi_{xx} \phi_z/2 + \partial_x^{-1} \phi_{zzz}/4 = 0$. This equation is obtained by unifying two directional generalization of the KdV equation, composing the closed ring with the KP equation and Bogoyavlenskii-Schiff equation. We also find the Miura transformation which yields the same ring in the corresponding modified equations.
{
"annotation_id": "338649d0-9a28-423e-9ddd-c35f2ae21af2",
"date_created": "2026-03-02T18:02:50.691000Z",
"date_modified": "2026-03-02T18:02:50.691000Z",
"file_hash": "acc68e8e246a0839e7fc9823258354c05026cb3545c53783f62c2d5e0346bd53",
"private": false,
"record": {
"abstract": "We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation,\n$\\phi_{xt} + \\phi_{xxxz}/4 + \\phi_x \\phi_{xz} + \\phi_{xx} \\phi_z/2 +\n\\partial_x^{-1} \\phi_{zzz}/4 = 0$. This equation is obtained by unifying two\ndirectional generalization of the KdV equation, composing the closed ring with\nthe KP equation and Bogoyavlenskii-Schiff equation. We also find the Miura\ntransformation which yields the same ring in the corresponding modified\nequations.",
"arxiv_id": "solv-int/9803012",
"authors": [
"S. J. Yu",
"K. Toda",
"T. Fukuyama"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/31/50/013",
"title": "N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation",
"url": "https://arxiv.org/abs/solv-int/9803012"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "89805621-dee8-470a-aa8b-e5d188c6d7fb",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}