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

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.

preprint2019arXivOpen access
Lijuan GuoJingsong HeLihong WangYi ChengD. J. FrantzeskakisP. G. Kevrekidis
nlin.SI
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Lijuan GuoJingsong HeLihong WangYi ChengD. J. FrantzeskakisP. G. Kevrekidis

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