Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
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In this paper, the Lax pair and Darboux transformation for the variable-coefficients coupled Hirota equations is constructed based on modulation instability and by taking the limit approach, two types of Nth-order rogue wave solutions with different dynamic structures in compact determinant representations.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2017-05-15 and is currently open access. It has received 60 citations till now. The article focuses on the topics: Rogue wave & Light intensity.read more
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Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber
TL;DR: In this article, a variable-coefficient coupled Hirota system is investigated, where the vector optical pulses in an inhomogeneous optical fiber are described by a Lax pair and a Darboux transformation.
Journal ArticleDOI
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.
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Dynamics of mixed lump-solitary waves of an extended (2 + 1)-dimensional shallow water wave model
Harun-Or-Roshid,Wen-Xiu Ma +1 more
TL;DR: In this paper, a ( 2 + 1 )-dimensional extended shallow water wave model is studied, based on its bilinear representation, and the impact of free parameters involved in the solutions on interaction types is exhibited.
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Localized waves and interaction solutions to an extended (3+1)-dimensional Jimbo–Miwa equation
TL;DR: Using Hirota bilinear method, four kinds of localized waves, solitons, breathers, lumps and rogue waves of the extended (3+1)-dimensional Jimbo–Miwa equation are constructed.
Journal ArticleDOI
Periodic and rational solutions of the reduced Maxwell-Bloch equations
TL;DR: The reduced Maxwell–Bloch equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions are investigated and Nth-order degenerate periodic and N third-order rational solutions containing several free parameters with compact determinant representations are derived.
References
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Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
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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.
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Water waves, nonlinear Schrödinger equations and their solutions
TL;DR: In this article, a number of ases in which these equations reduce to a one dimensional nonlinear Schrodinger (NLS) equation are enumerated, and several analytical solutions of NLS equations are presented, with discussion of their implications for describing the propagation of water waves.
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Waves that appear from nowhere and disappear without a trace
TL;DR: In this article, a hierarchy of rational solutions of the nonlinear Schrodinger equation (NLSE) with increasing order and with progressively increasing amplitude is presented. And the authors apply the WANDT title to two objects: rogue waves in the ocean and rational solution of the NLSE.
Journal ArticleDOI
Physical Mechanisms of the Rogue Wave Phenomenon
Christian Kharif,Efim Pelinovsky +1 more
TL;DR: A review of physical mechanisms of the rogue wave phenomenon is given in this article, where the authors demonstrate that freak waves may appear in deep and shallow waters and demonstrate that these mechanisms remain valid but should be modified.
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