Stable light-bullet solutions in the harmonic and parity-time-symmetric potentials

Dai, Chao-Qing; Wang, Xiaogang; Zhou, Guoquan

doi:10.1103/physreva.89.013834

Cited by 187 publications

(91 citation statements)

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“…In the past several decades, many e ective methods have been proposed for obtaining exact solutions of nonlin-*Corresponding Author: Sheng Zhang: School of Mathematics and Physics, Bohai University, Jinzhou 121013, PR China, E-mail: szhangchina@126.com Xu-Dong Gao: School of Mathematics and Statistics, Kashgar University, Kashgar 844066, Peoples's Republic of China ear PDEs, such as the inverse scattering transformation (IST) [1], Hirota's bilinear method [2], Bäcklund transformation [3,4], Painlevé expansion [5], homogeneous balance method [6], similarity transformation method [7,8], ansatz method [9,10], function expansion methods, and some others [11][12][13][14][15][16][17]. Among these methods, the IST [1] is a systematic method.…”

Section: Introductionmentioning

confidence: 99%

Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions

Zhang

Gao

2015

Open Physics

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Abstract:In this paper, the AKNS isospectral problem and its corresponding time evolution are generalized by embedding three coe cient functions. Starting from the generalized AKNS isospectral problem, a mixed spectral AKNS hierarchy with variable coe cients is derived. Thanks to the selectivity of these coe cient functions, the mixed spectral AKNS hierarchy contains not only isospectral equations but also nonisospectral equations. Based on a systematic analysis of the related direct and inverse scattering problems, exact solutions of the mixed spectral AKNS hierarchy are obtained through the inverse scattering transformation. In the case of re ectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. This paper shows that the AKNS spectral problem being nonisospectral is not a necessary condition to construct a nonisospectral AKNS hierarchy and that the inverse scattering transformation can be used for solving some other variable-coe cient mixed hierarchies of isospectral equations and nonisospectral equations.

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Section: Introductionmentioning

confidence: 99%

Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions

Zhang

Gao

2015

Open Physics

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“…On the other hand, it has been shown that the combinated influence of diffraction and chromatic dispersion leads to the formation of three dimensional localized structures often called light bullet [110,111,112,113]. We plan in the future to investigate the effect of delayed feedback on the spontaneous motion of three dimensional light bullets.…”

Section: Discussionmentioning

confidence: 99%

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

Tlidi

Averlant

Vladimirov

et al. 2015

Springer Proceedings in Physics

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We investigate the space-time dynamics of a Vertical-Cavity SurfaceEmitting Laser (VCSEL) subject to optical injection and to delay feedback control. Apart from their technological advantages, broad area VCSELs allow creating localized light structures (LSs). Such LSs, often called Cavity Solitons, have been proposed to be used in information processing, device characterization, and others. After a brief description of the experimental setup, we present experimental evidence of stationary LSs. We then theoretically describe this system using a mean field model. We perform a real order parameter description close to the nascent bistability and close to large wavelength pattern forming regime. We theoretically characterize the LS snaking bifurcation diagram in this framework. The main body of this chapter is devoted to theoretical investigations on the time-delayed feedback control of LSs in VCSELs. The feedback induces a spontaneous motion of the LSs, which we characterize by computing the velocity and the threshold associated with such motion. In the nascent bistability regime, the motion threshold and the velocity

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“…The types of the solitary waves with associated parametric constraints have been listed in Table 1. Finally, all of those parametric constraints can be referred to the free unknown quantities k, A 0 , ρ 0 with u 0 , the arbitrary integration constant c 0 , and the coefficient parameters a, b, c with d. We hope our investigation in this paper maybe useful for the study of other nonlinear models [34][35][36][37].…”

Section: Solitary Wave Types For Stationary Gardner Eq (7) Parametrimentioning

confidence: 97%

Madelung fluid description on a generalized mixed nonlinear Schrödinger equation

Lü

2015

Nonlinear Dyn

105

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Within the framework of the Madelung fluid description, in the present paper, we will derive bright and dark (including gray-and black-soliton) envelope solutions for a generalized mixed nonlinearby virtue of the corresponding solitary wave solutions for the generalized stationary Gardner equations. Via corresponding parametric constraints, our results are achieved under suitable assumptions for the current velocity associated with different boundary conditions of the fluid density ρ, while we have only considered the motion with stationary-profile current velocity case and excluded the motion with constant current velocity case. Note that our model is a generalized one with the inclusion of multiple coefficients (a, b, c and d).

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Stable light-bullet solutions in the harmonic and parity-time-symmetric potentials

Cited by 187 publications

References 50 publications

Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions

Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

Madelung fluid description on a generalized mixed nonlinear Schrödinger equation

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