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Title: Dam break problem for the focusing nonlinear Schrodinger equation and the generation of rogue waves
Authors: El, G.A.
Khamis, E.G.
Tovbis, Alexander
Issue Date: 2016
Publisher: © IOP Publishing Ltd & London Mathematical Society
Citation: EL, G.A., KHAMIS, E.G. and TOVBIS, A., 2016. Dam break problem for the focusing nonlinear Schrodinger equation and the generation of rogue waves. Nonlinearity, 29 (9), pp. 2798-2836
Abstract: We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrodinger (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.
Description: This is an author-created, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0951-7715/29/9/2798
Version: Accepted for publication
DOI: 10.1088/0951-7715/29/9/2798
URI: https://dspace.lboro.ac.uk/2134/22192
Publisher Link: http://dx.doi.org/10.1088/0951-7715/29/9/2798
ISSN: 1361-6544
Appears in Collections:Published Articles (Maths)

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