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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/22192

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 paper is in closed access until August 2017.
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:Closed Access (Maths)

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