Journal ArticleDOI
Rogue waves for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in an inhomogeneous optical fiber
TLDR
In this article, the effects of the group velocity dispersion coefficient and the fourth-order nonlinear Schrodinger equation on the first-order and second-order rogue wave solutions were analyzed.Abstract:
In this paper, investigation is made on the coupled variable-coefficient fourth-order nonlinear Schrodinger equations, which describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Via the generalized Darboux transformation, the first- and second-order rogue wave solutions are constructed. Based on such solutions, effects of the group velocity dispersion coefficient and the fourth-order dispersion coefficient on the rogue waves are graphically analyzed. The first-order rogue waves with the eye-shaped distribution, the interactions between the first-order rogue waves with solitons, and the second-order rogue waves with one highest peak and with the triangular structure are displayed. When the value of the group velocity dispersion coefficient or the fourth-order dispersion increases, range of the first-order rogue wave increases. Composite rogue waves are obtained, where the temporal separation between two adjacent rogue waves can be changed if we adjust the group velocity dispersion coefficient and fourth-order dispersion coefficient. Periodic rogue waves are presented. Periods of such rogue waves decrease with the periods of the group-velocity dispersion and fourth-order dispersion coefficient decreasing.read more
Citations
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Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations
TL;DR: On the higher-order Boussinesq-Burgers system, symbolic computation helps to go from the two-dimensional Bell polynomials to construct two non-auto-Backlund transformations and to proceed from the Painleve- backlund format to obtain four auto-Back Lund transformations with some soliton solutions.
Journal ArticleDOI
Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows
TL;DR: A generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows, is investigated, and the Darboux and generalizedDarboux transformations are derived, both relevant to the coefficient of the nonlinear term and coefficient related to the shear.
Journal ArticleDOI
Breather and hybrid solutions for a generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation for the water waves
TL;DR: In this paper, a generalized B-dimensional Kadomtsev-Petviashvili equation for the water waves is investigated, and two kinds of the hybrid solutions composed of the breathers, lumps, line rogue waves and kink solitons are given.
Journal ArticleDOI
One-soliton shaping and two-soliton interaction in the fifth-order variable-coefficient nonlinear Schrödinger equation
TL;DR: In this article, one-and two-soliton analytical solutions of a fifth-order nonlinear Schrodinger equation with variable coefficients are derived by means of the Hirota bilinear method.
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Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics
TL;DR: In this article, the authors derived the Nth-order Pfaffian solution to the Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics.
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.
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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.
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Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions.
Boling Guo,Liming Ling,Q. P. Liu +2 more
TL;DR: A generalized Darboux transformation for the nonlinear Schrödinger equation is constructed and the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.
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Solutions of the Vector Nonlinear Schrödinger Equations: Evidence for Deterministic Rogue Waves
TL;DR: A semirational, multiparametric vector solution of coupled nonlinear Schrödinger equations (Manakov system) is constructed that includes known vector Peregrine solutions, bright- and dark-rogue solutions, and novel vector unusual freak waves.
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Exact first-order solutions of the nonlinear Schrödinger equation
TL;DR: In this paper, a method for finding exact solutions of the nonlinear Schroedinger equations is proposed, in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time.