Journal ArticleDOI
Dynamics of breather waves and higher-order rogue waves in a coupled nonlinear Schrödinger equation
TLDR
In this paper, a coupled nonlinear Schrodinger (NLS) equation can be reduced to the generalized NLS equation by constituting a certain constraint and a generalized Darboux transformation (DT) is constructed.Abstract:
We consider a coupled nonlinear Schrodinger (NLS) equation, which can be reduced to the generalized NLS equation by constituting a certain constraint. We first construct a generalized Darboux transformation (DT) for the coupled NLS equation. Then, by using the resulting DT, we analyse the solutions with vanishing boundary condition and non-vanishing boundary condition, respectively, including positon wave, breather wave and higher-order rogue wave solutions for the coupled NLS equation. Moreover, in order to better understand the dynamic behavior, the characteristics of these solutions are discussed through some diverting graphics under different parameters choices.read more
Citations
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Journal ArticleDOI
The three-component coupled nonlinear Schrödinger equation: Rogue waves on a multi-soliton background and dynamics
Xiu-Bin Wang,Bo Han +1 more
Journal ArticleDOI
Characteristics of rogue waves on a periodic background for the Hirota equation
TL;DR: In this paper, the rogue dn-periodic waves (the rogue wave solutions on the dnperiodic wave background) for the Hirota equation by using Darboux transformation were considered.
Journal ArticleDOI
On the quintic time-dependent coefficient derivative nonlinear Schrödinger equation in hydrodynamics or fiber optics
TL;DR: In this article, a quintic time-dependent coefficient derivative nonlinear Schrodinger equation for certain hydrodynamic wave packets or a medium with the negative refractive index is investigated, and a gauge transformation is found to obtain the equivalent form of the equation.
Journal ArticleDOI
Rational and semi-rational solutions of a nonlocal (2 + 1)-dimensional nonlinear Schrödinger equation
Journal ArticleDOI
Dynamics of the soliton waves, breather waves, and rogue waves to the cylindrical Kadomtsev-Petviashvili equation in pair-ion-electron plasma
TL;DR: In this paper, a cylindrical Kadomtsev-Petviashvili (CKP) equation is derived from pair-ion-electron plasmas.
References
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Book
Nonlinear Fiber Optics
TL;DR: The field of nonlinear fiber optics has advanced enough that a whole book was devoted to it as discussed by the authors, which has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field.
Book
Optical solitons : from fibers to photonic crystals
TL;DR: In this article, the authors introduce spatial and temporal solitons in photonic crystals, and introduce the concept of Incoherent Solitons, which is a subclass of the spatial and temporally soliton.
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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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Rogue waves emerging from the resonant interaction of three waves.
TL;DR: A novel family of analytic solutions of the three-wave resonant interaction equations for the purpose of modeling unique events, i.e., "amplitude peaks" which are isolated in space and time are introduced.
Journal ArticleDOI
On the evolution of a rogue wave along the orthogonal direction of the ($t,x$)-plane
TL;DR: In this paper, the authors studied the evolution of the contour line with height c 2 + d along the orthogonal direction of the ( t, x )-plane for a first-order rogue wave solution u of the Kundu-Eckhaus equation.
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