Surfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon Equations

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dc.creatorBelich, H.
dc.creatorCuba, G.
dc.creatorPaunov, R.
dc.date1999-09-20
dc.date1999-11-22
dc.date.accessioned2026-07-07T06:17:53Z
dc.date.available2026-07-07T06:17:53Z
dc.descriptionBy 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-Bäcklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitly.
dc.descriptionlatex file, 23 pages, uses ams.tex
dc.identifierhttps://arxiv.org/abs/solv-int/9909018
dc.identifierhttp://arxiv.org/abs/solv-int/9909018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94546
dc.subjectExactly Solvable and Integrable Systems
dc.titleSurfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon Equations
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