Title

Dam Break Problem For The Focusing Nonlinear Schrödinger Equation And The Generation Of Rogue Waves

Keywords

modulation theory; nonlinear Schrödinger equation; Riemann-Hilbert problem; rogue waves; semi-classical limit

Abstract

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.

Publication Date

8-5-2016

Publication Title

Nonlinearity

Volume

29

Issue

9

Number of Pages

2798-2836

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0951-7715/29/9/2798

Socpus ID

84987933088 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84987933088

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