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.

• Received 19 May 2009

DOI:https://doi.org/10.1103/PhysRevE.80.026601

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Physical Review E 25th Anniversary Milestones

The year 2018 marks the 25th anniversary of Physical Review E. To celebrate the journal’s rich legacy, during the upcoming year we highlight a series of papers that made important contributions to their field. These milestone articles were nominated by members of the Editorial Board of Physical Review E, in collaboration with the journal’s editors. The 25 milestone articles, including an article for each calendar year from 1993 through 2017 and spanning all major subject areas of the journal, will be unveiled in chronological order and will be featured on the journal website.