Solutions of the Sinh-Gordon and Sine-Gordon equations and applications
Giannis Polychrou
TL;DR
This paper introduces new solutions to the elliptic sinh-Gordon and sine-Gordon equations using Bäcklund transformations and applies these solutions to construct novel harmonic maps between surfaces of constant negative curvature.
Contribution
It presents new solution families for elliptic sinh-Gordon and sine-Gordon equations and demonstrates their application in geometric surface mappings.
Findings
New solution families for elliptic sinh-Gordon and sine-Gordon equations
Construction of harmonic maps between surfaces of curvature -1
Use of Bäcklund transformations to connect equations
Abstract
We study the elliptic sinh-Gordon and sine-Gordon equations on the real plane and we introduce new families of solutions. We use a Backlund transformation that connects the elliptic versions of sinh-Gordon and sine-Gordon equations. As an application, we construct new harmonic maps between surfaces, when the target is of constant curvature -1.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Advanced Mathematical Physics Problems