Rogue waves and rational solutions of the nonlinear Schrödinger equation.
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.
Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
Nail
N
Akhmediev
Adrian
A
Ankiewicz
J M
JM
Soto-Crespo