Two-dimensional rogue waves on zero background of the Davey-Stewartson II equation
Abstract
A prototypical example of a rogue wave structure in a two-dimensional model is presented in the context of the Davey-Stewartson~II (DS~II) equation arising in water waves. The analytical methodology involves a Taylor expansion of an eigenfunctionof the model's Lax pair which is used to form a hierarchy of infinitely many new eigenfunctions. These are used for the construction of two-dimensional (2D) rogue waves (RWs) of the DS~II equation by the even-fold Darboux transformation (DT). The obtained 2D RWs, which are localized in both space and time, can be viewed as a 2D analogue of the Peregrine soliton and are thus natural candidates to describe oceanic RW phenomena,as well as ones in 2D fluid systems and water tanks.
Keywords
Cite
@article{arxiv.1905.11541,
title = {Two-dimensional rogue waves on zero background of the Davey-Stewartson II equation},
author = {Lijuan Guo and Jingsong He and Lihong Wang and Yi Cheng and D. J. Frantzeskakis and P. G. Kevrekidis},
journal= {arXiv preprint arXiv:1905.11541},
year = {2020}
}
Comments
6 pages, 3 color figures