A generating mechanism for higher order rogue waves
Exactly Solvable and Integrable Systems
2015-06-11 v5 Mathematical Physics
math.MP
Abstract
We introduce a mechanism for generating higher order rogue waves (HRWs) of the nonlinear Schr\"odinger(NLS) equation: the progressive fusion and fission of degenerate breathers associated with a critical eigenvalue , creates an order HRW. By adjusting the relative phase of the breathers at the interacting area, it is possible to obtain different types of HRWs. The value is a zero point of the eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order HRW.
Keywords
Cite
@article{arxiv.1209.3742,
title = {A generating mechanism for higher order rogue waves},
author = {J. S. He and H. R. Zhang and L. H. Wang and K. Porsezian and A. S. Fokas},
journal= {arXiv preprint arXiv:1209.3742},
year = {2015}
}
Comments
12 pages, 13 figures, To appear in Phys.Rev.E