Non-linear evolution equations and hyperelliptic covers of elliptic curves
Armando Treibich (LML)
TL;DR
This paper investigates spectral curves linked to doubly-periodic solutions of integrable equations like Korteweg-de Vries and Non-linear Schrödinger, constructing examples of arbitrary genus to understand their geometric properties.
Contribution
It provides a comprehensive analysis of spectral curves and constructs explicit examples of arbitrary genus hyperelliptic covers of elliptic curves.
Findings
Spectral curves exhibit specific properties related to integrable systems.
Construction methods for hyperelliptic covers of arbitrary genus.
Insights into the geometric structure of solutions to integrable equations.
Abstract
We study the general properties of spectral curves associated to doubly-periodic solutions of Korteweg-deVries, sine-Gordon, Non-linear Schr\"odinger and 1D Toda equations, and construct examples of arbitrary genus.
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