New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation

We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gor...

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Veröffentlicht in:	Revista matemática complutense 2024-09, Vol.37 (3), p.833-859
Hauptverfasser:	Polychrou, G., Papageorgiou, E., Fotiadis, A., Daskaloyannis, C.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Topology
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.
ISSN:	1139-1138 1988-2807
DOI:	10.1007/s13163-023-00476-z