General rogue waves in the focusing and defocusing Ablowitz-Ladik equations

2014/02/07 by Yasuhiro Ohta, Jianke Yang · 3 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1088/1751-8113/47/25/255201

24 pages, 6 figures

arxiv created 2014/02/07 · arxiv updated 2015/06/18

Abstract

General rogue waves in the focusing and defocusing Ablowitz-Ladik equations are derived by the bilinear method. In the focusing case, it is shown that rogue waves are always bounded. In addition, fundamental rogue waves reach peak amplitudes which are at least three times that of the constant background, and higher-order rogue waves can exhibit patterns such as triads and circular arrays with different individual peaks. In the defocusing case, it is shown that rogue waves also exist. In addition, these waves can blow up to infinity in finite time.

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• Swinging Waves in the Ablowitz-Ladik Equation
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