2015/05/31 by Gennady A. El, Eduardo G. Khamis, Alexander Tovbis · 2 citations
Physics and Astronomy · #nlin.PS #nlin.SI
paper · pdf · doi:10.1088/0951-7715/29/9/2798
published as Nonlinearity, 29 (2016) 2798-2836 · 29 pages, 15 figures, major revision
arxiv created 2016/05/01 · arxiv updated 2018/03/06
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (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.