Spectral data for simply periodic solutions of the sinh-gordon equation

Abstract

We now suppose that a simply periodic solution u: X→ ℂ of the sinh-Gordon equation △ u+ sinh (u) = 0 on an (open or closed) domain X⊂ ℂ is given. Without loss of generality, we suppose that 0 ∈ X and that 1 ∈ ℂ is the period of u.