English

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