Light bullet formation in a cubic-quintic nonlinear medium

Jovanoski, Zlatko

doi:10.1080/09500340010011745

Cited by 4 publications

(5 citation statements)

References 16 publications

(28 reference statements)

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“…Lastly, it is relevant to mention that the shape of the fundamental solitons which do not yet feature an extended flat-top profile, may be accurately predicted by the variational approximation based on the Gaussian ansatz, U (r) = A exp −r 2 /W 2 , with constants A and W representing the soliton's amplitude and width. These results are not displayed here in detail, as the approximation is similar to that developed previously for the NLSE with the CQ nonlinearity in 1D [20,46], 2D [23], and 3D [25] settings.…”

Section: The Modelmentioning

confidence: 52%

Interactions of three-dimensional solitons in the cubic-quintic model

Burlak

Malomed

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We report results of a systematic numerical analysis of interactions between three-dimensional (3D) fundamental solitons, performed in the framework of the nonlinear Schrödinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity, combining the self-focusing and defocusing terms. The 3D NLSE with the CQ terms may be realized in terms of spatiotemporal propagation of light in nonlinear optical media, and in Bose-Einstein condensates, provided that losses may be neglected. The first part of the work addresses interactions between identical fundamental solitons, with phase shift φ between them, separated by a finite distance in the free space. The outcome strongly changes with the variation of φ: in-phase solitons with φ = 0, or with sufficiently small φ, merge into a single fundamental soliton, with weak residual oscillations in it (in contrast to the merger into a strongly oscillating breather, which is exhibited by the 1D version of the same setting), while the choice of φ = π leads to fast separation between mutually repelling solitons. At intermediate values of φ, such as φ = π/2, the interaction is repulsive too, breaking the symmetry between the initially identical fundamental solitons, there appearing two solitons with different total energies (norms). The symmetry-breaking effect is qualitatively explained, similar to how it was done previously for 1D solitons. In the second part of the work, a pair of fundamental solitons trapped in a 2D potential is considered. It is demonstrated that they may form a slowly rotating robust "molecule," if initial kicks are applied to them in opposite directions, perpendicular to the line connecting their centers.

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Section: The Modelmentioning

confidence: 52%

Interactions of three-dimensional solitons in the cubic-quintic model

Burlak

Malomed

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In Figs. 1(a) and (b) we plot 20,30,60,100) and quintic nonlinearity q = 30. (b)The same for different quintic nonlinearities q (= 10, 30, 60, 100) and cubic nonlinearity p = 60.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Dispersion management can stabilize light bullets in a medium with cubic nonlinearity [19]. There has been variational study of light bullets in a cubic-quintic medium [20] where a condition of stability was obtained. Another study suggested a way of the stabilization of light bullets in a cubic-quintic medium by a periodic variation of diffraction and dispersion [21].…”

Section: Introductionmentioning

confidence: 99%

Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium

Adhikari

2016

Phys. Rev. E

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We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity. The 3D light bullet can propagate with a constant velocity in any direction. Stability of the light bullet under a small perturbation is established numerically. We consider frontal collision between two light bullets with different relative velocities. At large velocities the collision is elastic with the bullets emerge after collision with practically no distortion. At small velocities two bullets coalesce to form a bullet molecule. At a small range of intermediate velocities the localized bullets could form a single entity which expands indefinitely leading to a destruction of the bullets after collision. The present study is based on an analytic Lagrange variational approximation and a full numerical solution of the 3D nonlinear Schrödinger equation.

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“…It would also be desirable to study similar effects in two dimensions for the cubic defocusing nonlinearity, since it is relevant for Bose-Einstein experiments like [38], see also [58] and references therein. Moreover, it would be worth considering the three dimensional cubic-quintic case, which supports top-flat stable spatiotemporal solitons [59,60] and vortices [59,61]. Their collsional dynamics has been analyzed in [62,63] but the dynamics of dark traveling waves has not been described yet.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light

2017

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We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.

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Light bullet formation in a cubic-quintic nonlinear medium

Cited by 4 publications

References 16 publications

Interactions of three-dimensional solitons in the cubic-quintic model

Interactions of three-dimensional solitons in the cubic-quintic model

Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium

Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light

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