dorsal/arxiv
View SchemaSurfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon Equations
| Authors | H. Belich, G. Cuba, R. Paunov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9909018 |
| URL | https://arxiv.org/abs/solv-int/9909018 |
Abstract
By studying the {\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie-B\"acklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitly.
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"date_created": "2026-03-02T18:02:51.155000Z",
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"abstract": "By studying the {\\it internal} Riemannian geometry of the surfaces of\nconstant negative scalar curvature, we obtain a natural map between the\nLiouville, and the sine-Gordon equations. First, considering isometric\nimmersions into the Lobachevskian plane, we obtain an uniform expression for\nthe general (locally defined) solution of both the equations. Second, we prove\nthat there is a Lie-B\\\"acklund transformation interpolating between Liouville\nand sine-Gordon. Third, we use isometric immersions into the Lobachevskian\nplane to describe sine-Gordon N-solitons explicitly.",
"arxiv_id": "solv-int/9909018",
"authors": [
"H. Belich",
"G. Cuba",
"R. Paunov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Surfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon Equations",
"url": "https://arxiv.org/abs/solv-int/9909018"
},
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"execution_id": "95bfcc42-1e21-4359-88d5-db54291fda0f",
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"variant": "snapshot-2026-03-01",
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