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.

arXiv comment15 pages, LaTeX

References in corpus (5)

• Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
• Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation
• Rogue waves of the Hirota and the Maxwell-Bloch equations
• High-order rogue waves for the Hirota equation
• Some comments on continuous symmetries of AKNS hierarchy equations and their solutions

Cited by in corpus (2)

• Multi-component AKNS systems
• Hirota bilinear forms of the AKNS($N$) systems