Solutions of the Sinh-Gordon and Sine-Gordon equations and applications
arXiv:2212.09546
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.
14 pages, to be published