Odyssey of Light in Nonlinear Optical Fibers

4 Continuous-discrete duality of the nonlinear Schrödinger and Ablowitz–Ladik rogue wave hierarchies

A. Ankiewicz, D. J. Kedziora and N. Akhmediev

4.1 Introduction

The nonlinear Schrödinger equation (NLSE) is a ubiquitous model for wave evolution in the presence of dispersion and self-phase modulation. It is applicable in fields ranging from oceanography [1, 2] and optics [3] to ionospheric wave beam propagation [4], and, more generally, describes the evolution of slowly varying quasi-monochromatic wave packets in weakly nonlinear media. Of course, the equation is only a first-order approximation for the physics that arise in many of these cases, yet it manages to depict real-world phenomena with surprising accuracy. Solitons [5], breathers ...