New examples of harmonic maps to the hyperbolic plane via B\"acklund transformation
Giannis Polychrou, Effie Papageorgiou, Anestis Fotiadis, Costas, Daskaloyannis
TL;DR
This paper develops a Bäcklund transformation framework to construct new harmonic maps from complex plane subsets to the hyperbolic plane, linking solutions of sinh-Gordon and sine-Gordon equations.
Contribution
It introduces a novel method using Bäcklund transformations to generate harmonic maps to the hyperbolic plane, expanding the solution space.
Findings
Constructed new harmonic maps using Bäcklund transformations.
Linked solutions of sinh-Gordon and sine-Gordon equations.
Enhanced understanding of harmonic map generation techniques.
Abstract
We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In \cite{FotDask}, harmonic maps are related to the sinh-Gordon equation and a B{\"a}cklund 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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Molecular spectroscopy and chirality · Quantum Mechanics and Non-Hermitian Physics