@Article{ElKhamTovb:2016:DaBrPr,
author = "El, G. A. and Khamis, Eduardo Georges and Tovbis, A.",
affiliation = "{Loughborough University} and {Instituto Nacional de Pesquisas
Espaciais (INPE)} and {University of Central Florida}",
title = "Dam break problem for the focusing nonlinear Schr{\"o}dinger
equation and the generation of rogue waves",
journal = "Nonlinearity",
year = "2016",
volume = "29",
pages = "2798--2836",
keywords = "nonlinear Schr{\"o}dinger equation, rogue waves, modulation
theory, semi-classical limit, Riemann–Hilbert problem.",
abstract = "We propose a novel, analytically tractable, scenario of the rogue
wave formation in the framework of the small-dispersion focusing
nonlinear Schr{\"o}dinger (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 trainsthe dispersive dam break flowsgenerated 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.",
doi = "10.1088/0951-7715/29/9/2798",
url = "http://dx.doi.org/10.1088/0951-7715/29/9/2798",
issn = "0951-7715",
language = "en",
targetfile = "Khamis_dam.pdf",
urlaccessdate = "28 abr. 2024"
}