Non-linear evolution equations and hyperelliptic covers of elliptic curves

Armando Treibich Kohn (1)

1 LML - Laboratoire de Mathématiques de Lens

We study the general properties of spectral curves associated to doubly-periodic solutions of Korteweg-deVries, sine-Gordon, Non-linear Schrödinger and 1D Toda equations, and construct examples of arbitrary genus.

Keywords: hyperelliptic d-osculating covers; rational surface; elliptic curve; Korteweg-de Vries; 1D Toda; Non-linear Schrödinger; sine-Gordon; doubly periodic

Domains: Algebraic Geometry [math.AG]; Analysis of PDEs [math.AP]

Armando Treibich Kohn. Non-linear evolution equations and hyperelliptic covers of elliptic curves. 2010. ⟨hal-00460434⟩