Summary: Rogue waves and rational solutions of the nonlinear Schrödinger equation
and J. M. Soto-Crespo2
Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University,
Canberra, Australian Capital Territory 0200, Australia
Instituto de Óptica, CSIC, Serrano 121, 28006 Madrid, Spain
Received 19 May 2009; published 4 August 2009
We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear
Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain
their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small
amplitude radiation waves. Our work can elucidate the appearance of rogue waves in the deep ocean and can
be applied to the observation of rogue light pulse waves in optical fibers.
DOI: 10.1103/PhysRevE.80.026601 PACS number s : 42.65. k, 47.20.Ky, 05.45.Yv
Rational solutions of the nonlinear Schrödinger equation
NLSE play a major role in the theory of rogue waves 1,2 .
There is a hierarchy of them with progressively increasing