Title: Spectral curves for the rogue waves,
Abstract: Here we find the spectral curves, corresponding to the known rational or
quasi-rational solutions of AKNS hierarchy equations, ultimately connected with
the modeling of the rogue waves events in the optical waveguides and in
hydrodynamics. We also determine spectral curves for the multi-phase
trigonometric, hyperbolic and elliptic solutions for the same hierarchy. It
seams that the nature of the related spectral curves was not sufficiently
discussed in existing literature.