Rogue waves and rational solutions of the nonlinear Schrödinger equation
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- 4 August 2009
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 80 (2) , 026601
- https://doi.org/10.1103/physreve.80.026601
Abstract
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.Keywords
This publication has 19 references indexed in Scilit:
- Extreme waves that appear from nowhere: On the nature of rogue wavesPublished by Elsevier ,2009
- Waves that appear from nowhere and disappear without a tracePhysics Letters A, 2009
- Can bottom friction suppress ‘freak wave’ formation?Journal of Fluid Mechanics, 2008
- Optical rogue wavesNature, 2007
- Physical mechanisms of the rogue wave phenomenonPublished by Elsevier ,2003
- Note on Breather Type Solutions of the NLS as Models for Freak-WavesPhysica Scripta, 1999
- Modulation instability and periodic solutions of the nonlinear Schr dinger equationTheoretical and Mathematical Physics, 1986
- Water waves, nonlinear Schrödinger equations and their solutionsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1983
- The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger EquationStudies in Applied Mathematics, 1979
- The disintegration of wave trains on deep water Part 1. TheoryJournal of Fluid Mechanics, 1967