General rogue waves in the focusing and defocusing Ablowitz-Ladik equations
Exactly Solvable and Integrable Systems
2015-06-18 v1
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.
Keywords
Cite
@article{arxiv.1402.1537,
title = {General rogue waves in the focusing and defocusing Ablowitz-Ladik equations},
author = {Yasuhiro Ohta and Jianke Yang},
journal= {arXiv preprint arXiv:1402.1537},
year = {2015}
}
Comments
24 pages, 6 figures