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 a direct variable transformation, the authors obtained multiple rogue wave solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation, including first-order, two-order and three-order solutions.
Abstract: Based on a direct variable transformation, we obtain multiple rogue wave solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation, including first-order, two-order and three-order rogue wave solutions. Their dynamic behaviors are shown by some 3D plots. Compared with Zha’s symbolic computation approach, we do not need to resort to Hirota bilinear form, and it can be used to deal with variable-coefficient integrable equations. Interaction solution between rogue wave and periodic wave is obtained by using the Hirota bilinear form. Abundant breather wave solutions are presented by a direct test function.
41 citations
TL;DR: In this paper, it is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble.
41 citations
TL;DR: In this article, a variable-coefficient generalized nonlinear Schrodinger equation is used to describe the nonlinear phenomena in the optical fiber, fluid or plasma, and three types of soliton interaction have been attained: the bound state, one bell-shape soliton catching up with the other and two bell-shaped soliton head-on interaction.
Abstract: In this paper, a variable-coefficient generalized nonlinear Schrodinger equation, which can be used to describe the nonlinear phenomena in the optical fiber, fluid or plasma, is investigated. Lax pair, higher-order rogue-wave and multi-soliton solutions, Darboux transformation and generalized Darboux transformation are obtained. Wave propagation and interaction are analyzed: (1) The Hirota and Lakshmanan–Porsezian–Daniel coefficients affect the propagation velocity and path of each one soliton; three types of soliton interaction have been attained: the bound state, one bell-shape soliton’s catching up with the other and two bell-shape soliton head-on interaction. Multi-soliton interaction is elastic. (2) The Hirota and Lakshmanan–Porsezian–Daniel coefficients affect the propagation direction of the first-step rogue waves and interaction range of the higher-order rogue waves.
41 citations
TL;DR: It is shown that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaoticWave field.
Abstract: In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrodinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.
41 citations
TL;DR: The integrable coupled nonlinear Schrödinger equations with four-wave mixing with complex dynamics and dynamics by different kinds of spatial–temporal distribution structures including triangular, pentagonal, ‘claw-like’ and heptagonal patterns are investigated.
Abstract: The integrable coupled nonlinear Schrodinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial–temporal distribution structures including triangular, pentagonal, ‘claw-like’ and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.
41 citations