Breather‐to‐soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

Sun, Wen‐Rong

doi:10.1002/andp.201600227

Cited by 27 publications

(13 citation statements)

References 34 publications

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“…However, our context will be adhering to the Peregrine soliton solutions realized for such HNLSEs with different higher-order dispersive and nonlinear effects under certain circumstances. Diverse HNLSEs have been reported in the literature, namely, the Hirota equation [111], the Lakshmanan-Porsezian-Daniel equation [110], the quintic NLSE [22], the sextic NLSE [112,113], heptic NLSE [112], and octic NLSE [112]. This section attempts to review the occurrence of the Peregrine solution reported in the aforementioned HNLSEs.…”

Section: Peregrine Solitons Of Higher-order and Inhomogeneous Nlsesmentioning

confidence: 99%

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

2020

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This study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems. The historical perspectives include the various analytical techniques developed for constructing the Peregrine soliton solutions, followed by the derivation of the general breather solution of the fundamental nonlinear Schrödinger equation through Darboux transformation. Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.

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Section: Peregrine Solitons Of Higher-order and Inhomogeneous Nlsesmentioning

confidence: 99%

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

2020

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“…[1][2][3][4][5][6] In plasma physics, Alfvén waves have been considered as a type of the magnetohydrodynamic waves in which the ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines. [7][8][9] In the framework of magnetohydrodynamics, Alfvén waves have been described by the DOI: 10.1002/andp.202100231 derivative nonlinear Schrödinger (DNLS) equation. [10][11][12][13][14] Real plasma environment has been shown to be inhomogeneous, which exhibits the fluctuations of density, temperature and magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

Odd‐Fold Darboux Transformation, Breather, Rogue‐Wave and Semirational Solutions on the Periodic Background for a Variable‐Coefficient Derivative Nonlinear Schrödinger Equation in an Inhomogeneous Plasma

2021

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Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a variable-coefficient derivative nonlinear Schrödinger equation describing the nonlinear Alfvén waves in an inhomogeneous plasma. With respect to the left polarized Alfvén wave, the odd-fold Darboux transformation, breather, rogue-wave and semirational solutions are constructed on the periodic background. Conditions for the antidark/gray/black soliton solutions or periodic solutions are obtained. Period of the Akhmediev breather is independent of the dispersion coefficient. When such an equation has a constant dispersion, with the increasing value of the dispersion coefficient, quasi-period of the Kuznetsov-Ma breather decreases, quasi-periods of the spatio-temporal breathers along the 𝝃 and 𝝉 axes both decrease and range of the rogue wave along the 𝝉 axis decreases, where 𝝃 and 𝝉 are the stretched time and space variables, respectively. When such an equation has a 𝝉-dependent linear dispersion, with the increasing value of |𝝉|, quasi-period of the Kuznetsov-Ma breather decreases and quasi-periods of the spatio-temporal breathers along the 𝝃 and 𝝉 axes both decrease. When such an equation has a constant loss/gain, linearly periodic background is exhibited. When such an equation has a 𝝉-dependent linear loss/gain, parabolic-periodic background is shown.

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“…When δ = 0, (1.2) will be reduced to the one-dimensional NLS equation. Some work of the sixticorder NLS equation have been investigated, such as breather solutions with imaginary eigenvalues and the interactions between two solitons of the sextic NLS equations (1.2) have been obtained in [6].…”

Section: Introductionmentioning

confidence: 99%

Inverse scattering transform and multi-solition solutions for the sextic nonlinear Schrödinger equation

Wu¹,

Tian²,

Yang³

2020

Preprint

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In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectrum problem are derived directly, and the scattering data with t = 0 are obtained according to analyze the symmetry and other related properties of the Jost functions. Then we take use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel'fand-Levitan-Marchenko (GLM) integral equations.Furthermore, the time evolution of scattering data is considered, on the basic of that, the multi-solition solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could be enriched the nonlinear phenomena of the sextic nonlinear Schrödinger equation.

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Breather‐to‐soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

Cited by 27 publications

References 34 publications

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

Odd‐Fold Darboux Transformation, Breather, Rogue‐Wave and Semirational Solutions on the Periodic Background for a Variable‐Coefficient Derivative Nonlinear Schrödinger Equation in an Inhomogeneous Plasma

Inverse scattering transform and multi-solition solutions for the sextic nonlinear Schrödinger equation

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