Perturbation-induced dynamics of dark solitons

Kivshar, Yuri S.; Yang, Xiaoping

doi:10.1103/physreve.49.1657

Cited by 160 publications

(132 citation statements)

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“…The background height and trough of the soliton (A(Z )) are accurately approximated by our method (figure 7a); this agrees with previously found approximations (Kivshar & Yang 1994). Our results for t 0 and s 0 are plotted in figure 7b.…”

Section: Linear Dampingsupporting

confidence: 79%

“…The method was extended to grey solitons and general perturbations but only for two of the four main soliton parameters; background height and soliton depth were determined. The evolution of the background was shown to be independent of the soliton by Kivshar & Yang (1994) and the asymptotic behaviour at infinity was used to separate the propagation of the background magnitude from the rest of the soliton. The amplitude/width of the soliton 'core' was determined via a perturbed Hamiltonian.…”

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confidence: 99%

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Perturbations of dark solitons

et al. 2011

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A direct perturbation method for approximating dark soliton solutions of the nonlinear Schrödinger (NLS) equation under the influence of perturbations is presented. The problem is broken into an inner region, where the core of the soliton resides, and an outer region, which evolves independently of the soliton. It is shown that a shelf develops around the soliton that propagates with speed determined by the background intensity. Integral relations obtained from the conservation laws of the NLS equation are used to determine the properties of the shelf. The analysis is developed for both constant and slowly evolving backgrounds. A number of problems are investigated, including linear and nonlinear damping type perturbations. Keywords: perturbation theory; solitons; opticsPerturbation theory as applied to solitons that decay at infinity, i.e. so-called bright solitons, has been developed over many years (cf. Karpman & Maslov 1977;Kodama & Ablowitz 1981;Herman 1990). The analytical work employs a diverse set of methods including perturbations of the inverse scattering transform (IST), multi-scale perturbation analysis, perturbations of conserved quantities, etc.; the analysis applies to a wide range of physical problems. In optics, a central equation that describes the envelope of a quasi-monochromatic wave train is the nonlinear Schrödinger (NLS) equation, which in normalized form readswhere D, n are constants. In this paper, we consider the NLS equation in a typical nonlinear optics context, where D corresponds to the group-velocity dispersion (GVD), n > 0 is related to the nonlinear index of refraction, z is the

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Section: Linear Dampingsupporting

confidence: 79%

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confidence: 99%

Perturbations of dark solitons

et al. 2011

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“…Eventually, further emission of radiation results again in the increase of the soliton's kinetic energy and the amplitude of oscillations increases. Note that at t = 2000 the soliton position is x ≈ −3.5, i.e., quite close to its initial location, while its amplitude is cos ϕ ≈ 0.95; thus, at that time, the soliton intensity defined as cos 2 ϕ [33], takes 90% of its initial value (recall that cos 2 ϕ(0) = 1).…”

Section: Intermediate Optical Lattice Periodmentioning

confidence: 99%

“…Next, assuming that the perturbation P is small indeed, we apply the perturbation theory for DSs, as developed in Ref. [33], to Eq. (5).…”

Section: The Long-period Optical Latticementioning

confidence: 99%

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Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Theocharis

Frantzeskakis

Kevrekidis

et al. 2005

Mathematics and Computers in Simulation

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We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.

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Solitons in Optical Fibers

Gordon¹

2022

Solitons in Optical Fiber Systems

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Perturbation-induced dynamics of dark solitons

Cited by 160 publications

References 49 publications

Perturbations of dark solitons

Perturbations of dark solitons

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Solitons in Optical Fibers

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