Darboux coordinates for periodic solutions of the sinh-Gordon equation

TL;DR

This paper investigates the space of periodic solutions to the elliptic sinh-Gordon equation using spectral data, establishing the existence of Darboux coordinates to better understand their structure.

Contribution

It introduces Darboux coordinates for the spectral data of periodic sinh-Gordon solutions, providing a new framework for their analysis.

Findings

Existence of Darboux coordinates for spectral data

Representation of solutions via Riemann surface and divisor

Enhanced understanding of the solution space structure

Abstract

We study the space of periodic solutions of the elliptic $\sinh$-Gordon equation by means of spectral data consisting of a Riemann surface $Y$ and a divisor $D$ and prove the existence of certain Darboux coordinates.