Journal ArticleDOI
Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation
Lian-Li Feng,Tian-Tian Zhang +1 more
TLDR
Based on the Lax pair of the coupled NLS equation, the determinant representation of the N -fold Darboux transformation(DT) was constructed in this paper, which obtained its higher-order soliton, breather and rogue wave solutions.About:
This article is published in Applied Mathematics Letters.The article was published on 2018-04-01. It has received 104 citations till now. The article focuses on the topics: Breather & Nonlinear Schrödinger equation.read more
Citations
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Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation
TL;DR: Using Bell’s polynomials and the extended homoclinic test theory, a bilinear form of the gBS equation is derived, which is explicitly constructed as a soliton solutions for the (2+1)-dimensional generalized breaking soliton equation.
Journal ArticleDOI
Complex wave structures for abundant solutions related to the complex Ginzburg–Landau model
TL;DR: In this article, the authors apply an analytical algorithm, namely the modified auxiliary equation method, to investigate the complex wave structures for abundant solutions related to the complex Ginzburg-Landau model.
Journal ArticleDOI
Rogue waves, bright–dark solitons and traveling wave solutions of the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation
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.
Journal ArticleDOI
On quasi-periodic waves and rogue waves to the (4+1)-dimensional nonlinear Fokas equation
TL;DR: In this article, an effective and straightforward method is presented to succinctly construct the bilinear representation of the (4+1)-dimensional nonlinear Fokas equation, which is an important physics model.
Journal ArticleDOI
Analytical and numerical simulations for the kinetics of phase separation in iron (Fe-Cr-X (X=Mo, Cu)) based on ternary alloys
Dianchen Lu,Mohamed S. Osman,Mohamed S. Osman,Mostafa M. A. Khater,Raghda A. M. Attia,Raghda A. M. Attia,Dumitru Baleanu +6 more
TL;DR: In this paper, the authors investigate the physical behavior of the basic elements that related to phase decomposition in ternary alloys of (FeCr-Mo) and (Fe-Cr-Cu) according to analytical and approximate simulation.
References
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Journal ArticleDOI
Optical rogue waves
TL;DR: This work reports the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input.
Journal ArticleDOI
The Peregrine soliton in nonlinear fibre optics
Bertrand Kibler,Julien Fatome,Christophe Finot,Guy Millot,Frédéric Dias,Frédéric Dias,Goëry Genty,Nail Akhmediev,John M. Dudley +8 more
TL;DR: The Peregrine soliton was observed experimentally for the first time by using femtosecond pulses in an optical fiber as mentioned in this paper, which gave some insight into freak waves that can appear out of nowhere before simply disappearing.
Journal ArticleDOI
On a class of physically important integrable equations
TL;DR: In this paper, a methodology introduced by Fuchssteiner and the author is used to derive a class of physically important integrable evolution equations, which are integrably generalizations of the Korteweg-deVries (KdV), of the modified KdV, of the nonlinear Schrodinger (NLS), and of the sine-Gordon equations.
Journal ArticleDOI
Extreme waves that appear from nowhere: On the nature of rogue waves
TL;DR: In this article, a plane wave is modulated by relatively weak random waves, and it is shown that the peaks with highest amplitude of the resulting wave composition can be described in terms of exact solutions of the focusing nonlinear Schrrodinger equation in the form of the collision of Akhmediev breathers.
Journal ArticleDOI
Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
Wen-Xiu Ma,Yuncheng You +1 more
TL;DR: A broad set of sufficient conditions consisting of systems of linear partial differential equations is presented which guarantees that the Wronskian determinant solves the Korteweg-de Vries equation in the bilinear form as mentioned in this paper.
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