author = "El, G. A. and Khamis, Eduardo Georges and Tovbis, A.",
          affiliation = "{Loughborough University} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {University of Central Florida}",
                title = "Dam break problem for the focusing nonlinear Schr{\"o}dinger 
                         equation and the generation of rogue waves",
              journal = "Nonlinearity",
                 year = "2016",
               volume = "29",
                pages = "2798--2836",
             keywords = "nonlinear Schr{\"o}dinger equation, rogue waves, modulation 
                         theory, semi-classical limit, Riemann–Hilbert problem.",
             abstract = "We propose a novel, analytically tractable, scenario of the rogue 
                         wave formation in the framework of the small-dispersion focusing 
                         nonlinear Schr{\"o}dinger (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 trainsthe dispersive dam break flowsgenerated 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 
                  doi = "10.1088/0951-7715/29/9/2798",
                  url = "http://dx.doi.org/10.1088/0951-7715/29/9/2798",
                 issn = "0951-7715",
             language = "en",
           targetfile = "Khamis_dam.pdf",
        urlaccessdate = "04 dez. 2020"