rogue_box_Nonlinearity_accepted.pdf (6.53 MB)
Dam break problem for the focusing nonlinear Schrodinger equation and the generation of rogue waves
journal contribution
posted on 2016-08-04, 10:05 authored by Gennady El, E.G. Khamis, Alexander TovbisWe 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.
History
School
- Science
Department
- Mathematical Sciences
Published in
NonlinearityCitation
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. 2798-2836Publisher
© IOP Publishing Ltd & London Mathematical SocietyVersion
- AM (Accepted Manuscript)
Acceptance date
2016-07-14Publication date
2016Notes
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/10.1088/0951-7715/29/9/2798ISSN
1361-6544Publisher version
Language
- en