dorsal/arxiv
View SchemaTau-function for discrete sine-Gordon equation and quantum R-matrix
| Authors | A. Zabrodin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9810003 |
| URL | https://arxiv.org/abs/solv-int/9810003 |
Abstract
We prove that the tau-function of the integrable discrete sine-Gordon model apart from the "standard" bilinar identities obeys a number of "non-standard" ones. They can be combined into a bivector 3-dimensional difference equation which is shown to contain Hirota's difference analogue of the sine-Gordon equation and both auxiliary linear problems for it. We observe that this equation is most naturally written in terms of the quantum R-matrix for the XXZ spin chain and looks then like a relation of the "vertex-face correspondence" type.
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"date_created": "2026-03-02T18:02:50.962000Z",
"date_modified": "2026-03-02T18:02:50.962000Z",
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"abstract": "We prove that the tau-function of the integrable discrete sine-Gordon model\napart from the \"standard\" bilinar identities obeys a number of \"non-standard\"\nones. They can be combined into a bivector 3-dimensional difference equation\nwhich is shown to contain Hirota\u0027s difference analogue of the sine-Gordon\nequation and both auxiliary linear problems for it. We observe that this\nequation is most naturally written in terms of the quantum R-matrix for the XXZ\nspin chain and looks then like a relation of the \"vertex-face correspondence\"\ntype.",
"arxiv_id": "solv-int/9810003",
"authors": [
"A. Zabrodin"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"title": "Tau-function for discrete sine-Gordon equation and quantum R-matrix",
"url": "https://arxiv.org/abs/solv-int/9810003"
},
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