Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

Gennady El, Eduardo Khamis, Alexander Tovbis

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41 Citations (Scopus)
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Abstract

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a 'box'). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.
Original languageEnglish
Pages (from-to)2798–2836
JournalNonlinearity
Volume29
Issue number9
Early online date5 Aug 2016
DOIs
Publication statusPublished - 1 Sep 2016
Externally publishedYes

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