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: Based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breathing wave solutions of the Kadomtsev–Petviashvili equation are well constructed.
Abstract: Under investigation in this work is a generalized ( 3 + 1 )-dimensional Kadomtsev–Petviashvili (GKP) equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of the Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solution. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breather wave solutions of the equation are well constructed. It is hoped that our results can be used to enrich the dynamical behavior of the ( 3 + 1 )-dimensional nonlinear wave fields.
73 citations
TL;DR: The Kadomtsev–Petviashvili equation is investigated, which describes the dynamics of nonlinear waves in plasma physics and fluid dynamics and a new family of two wave solutions, rational breather wave and rogue wave solutions of the equation is constructed.
Abstract: In this paper, a ( 3 + 1 ) -dimensional generalized Kadomtsev–Petviashvili (gKP) equation is investigated, which describes the dynamics of nonlinear waves in plasma physics and fluid dynamics. By employing the extended homoclinic test method, we construct a new family of two wave solutions, rational breather wave and rogue wave solutions of the equation. Moreover, by virtue of some ansatz functions and the Riccati equation method, its analytical bright soliton, dark soliton and traveling wave solutions are derived. Finally, we obtain its exact power series solution with the convergence analysis. In order to further understand the dynamics, we provide some graphical analysis of these solutions.
73 citations
TL;DR: In this paper, the authors provide a new perspective on the nonlinear wave dynamics for this problem in the particular case of unidirectional wave propagation, based upon the well-known nonlinear Schroedinger equation that governs the space/time dynamics of narrow banded, deep-water wave trains to leading order in cubic nonlinearity.
72 citations
TL;DR: In this article, the authors derived probability distributions for height and period for the highest wave occurring at a fixed location when the sea state varies, using a data base of waverider data from the Norwegian Sea.
72 citations
TL;DR: In this article, a semi-classical model of the rogue wave formation was proposed 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").
Abstract: 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.
72 citations