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arXiv · 1905.11541

Two-dimensional rogue waves on zero background of the Davey-Stewartson II equation

Lijuan Guo·Jingsong He·Lihong Wang·Yi Cheng·D. J. Frantzeskakis·P. G. Kevrekidis
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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.

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Lijuan Guo, Jingsong He, Lihong Wang, Yi Cheng, D. J. Frantzeskakis, P. G. Kevrekidis. 2019-05-27. Two-dimensional rogue waves on zero background of the Davey-Stewartson II equation. https://doi.org/10.1103/physrevresearch.2.033376

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