Topic
Rogue wave
About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.
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TL;DR: In this paper, the authors investigated higher-order rogue wave solutions of the Kundu-Eckhaus equation, which contains quintic nonlinearity and the Raman effect in nonlinear optics.
Abstract: In this paper, we investigate higher-order rogue wave solutions of the Kundu–Eckhaus equation, which contains quintic nonlinearity and the Raman effect in nonlinear optics. By means of a gauge transformation, the Kundu–Eckhaus equation is converted to an extended nonlinear Schrodinger equation. We derive the Lax pair, the generalized Darboux transformation, and the Nth-order rogue wave solution for the extended nonlinear Schrodinger equation. Then, by using the gauge transformation between the two equations, a concise unified formula of the Nth-order rogue wave solution with several free parameters for the Kundu–Eckhaus equation is obtained. In particular, based on symbolic computation, explicit rogue wave solutions to the Kundu–Eckhaus equation from the first to the third order are presented. Some figures illustrate dynamic structures of the rogue waves from the first to the fourth order. Moreover, through numerical calculations and plots, we show that the quintic and Raman-effect nonlinear terms affect the spatial distributions of the humps in higher-order rogue waves, although the amplitudes and the time of appearance of the humps are unchanged.
91 citations
TL;DR: In this article, the authors analyzed the sea state conditions during which the accident of the cruise ship Louis Majesty took place, showing that the angle between the two wave systems during the accident was close to the condition for which the maximum amplitude of the breather solution is observed.
Abstract: [1] We analyze the sea state conditions during which the accident of the cruise ship Louis Majesty took place. The ship was hit by a large wave that destroyed some windows at deck number five and caused two fatalities. Using the wave model (WAM), driven by the Consortium for Small-Scale Modelling (COSMO-ME) winds, we perform a detailed hindcast of the local wave conditions. The results reveal the presence of two comparable wave systems characterized almost by the same frequency. We discuss such sea state conditions in the framework of a system of two coupled Nonlinear Schrodinger (CNLS) equations, each of which describe the dynamics of a single spectral peak. For some specific parameters, we discuss the breather solutions of the CNLS equations and estimate the maximum wave amplitude. Even though, due to the lack of measurements, it is impossible to establish the nature of the wave that caused the accident, we show that the angle between the two wave systems during the accident was close to the condition for which the maximum amplitude of the breather solution is observed.
91 citations
TL;DR: In this paper, the authors numerically investigate dispersive perturbations of the nonlinear Schrodinger (NLS) equation, which model waves in deep water, and observe that a chaotic regime greatly increases the likelihood of rogue wave formation.
90 citations
TL;DR: Breathers and rogue waves as exact solutions of a nonlocal partial differential equation of the third order are derived by a bilinear transformation and demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.
89 citations
TL;DR: Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrodinger equation with nonzero boundary is given using the elementary Darboux transformation but not with the limit progress, which is more convenient than before.
89 citations