Dam break problem for the focusing nonlinear Schrodinger equation and the generation of rogue waves
Gennady El
E.G. Khamis
Alexander Tovbis
2134/22192
https://repository.lboro.ac.uk/articles/Dam_break_problem_for_the_focusing_nonlinear_Schrodinger_equation_and_the_generation_of_rogue_waves/9388136
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.
2016-08-04 10:05:19
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