Non-autonomous solitons in inhomogeneous nonlinear media with distributed dispersion

Kengne, Emmanuel; Lakhssassi, Ahmed; Liu, Wu-Ming

doi:10.1007/s11071-019-04991-x

Cited by 37 publications

(25 citation statements)

References 72 publications

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“…)Z, and other parameters ζ, X and Z are as given in Eq. (14). This IICS admits well-known bell-type/symmetric-single-hump profile with certain amplitude B j , width (proportional to inverse of amplitude), and velocity 2δk 1I of propagation represented by the above form.…”

Section: Inhomogeneous Incoherently Coupled Solitonsmentioning

confidence: 99%

“…From the above general one-soliton solution (14), one can easily understand that the choice S 1 = 0 leads to e δ (1) 11 and e 11 vanish. This results into a simple form corresponding to that of Manakov type solitons without the contribution from coherent nonlinearity, which can be designated as inhomogeneous incoherently coupled solitons (IICSs).…”

Section: Inhomogeneous Incoherently Coupled Solitonsmentioning

confidence: 99%

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Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

Mareeswaran

Sakkaravarthi

Kanna³

2020

J. Phys. A: Math. Theor.

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We investigate non-autonomous solitons in a general coherently coupled nonlinear Schrödinger (CC-NLS) system with temporally modulated nonlinearities and with an external harmonic oscillator potential. This general CCNLS system encompasses three distinct types of CCNLS equations that describe the dynamics of beam propagation in an inhomogeneous Kerr-like nonlinear optical medium for different choices of nonlinear polarizations owing to the anisotropy of the medium. We identify a generalized similarity transformation to relate the considered model into the standard integrable homogeneous coupled nonlinear evolution equations with constant nonlinearities, accompanied by a constraint relation expressed in the form of the Riccati equation. With the help of a non-standard Hirota's bilinearization method and exact soliton solutions, we explore the impact of varying nonlinearities and refractive index in the propagation and collisions analytically by reverse engineering. Interestingly, we show the emergence of several modulated solitonic phenomena such as periodic oscillation, amplification, compression, tunneling/cross-over, excitons, as well as their combined effect in the single-soliton propagation and two-soliton collisions with appropriate forms of nonlinearity. Notably, we identify a tool to transform the nature of soliton collisions with certain type of inhomogeneous nonlinearities. The results could be of significant interest to the studies on management of nonlinear waves in the contexts like nonlinear optics and can also be extended to Bose-Einstein condensates and super-fluids.

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Section: Inhomogeneous Incoherently Coupled Solitonsmentioning

confidence: 99%

Section: Inhomogeneous Incoherently Coupled Solitonsmentioning

confidence: 99%

Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

Mareeswaran

Sakkaravarthi

Kanna³

2020

J. Phys. A: Math. Theor.

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“…(37)-(38d) that β is constant, while α(t) and g 0 (t) satisfy the nonlinear second-order ODE, Thus, in the special case of constant λ 0 , λ and β, the problem of finding (t), η(t), and T (t) amounts to solving Eq. (49). The simplest possibility is to solve it for α(t) if g 0 (t) is known.…”

Section: Modulational Instability In the Inhomogeneous Cubic Derivatimentioning

confidence: 99%

“…The FR can also be imposed optically, by appropriate laser illumination [39][40][41][42], as well as by microwave [43] and electrostatic [44] fields. Then, NM for BEC may be realized using time-dependent and/or nonuniform control fields [4,8,40,41,[45][46][47]49]. In particular, the FR technique makes it possible to quickly reverse (in time) the interaction sign from repulsion to attraction (positive to negative scattering length), which gives rise, via the onset of the collapse, to abrupt shrinkage of the condensate, followed by a burst of emitted atoms and the formation of a stable residual condensate [50].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal engineering of matter-wave solitons in Bose–Einstein condensates

2021

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• A review is focused on 1D, 2D, and 3D matter-wave solitons in Bose-Einstein condensates under the action of spatiotemporally modulated cubic nonlinearity and time-dependent trapping potentials • Most essential problems under the consideration is the shape and stability of solitons and other coherent structures, including stabilization against the critical collapse • Both analytical results (exact and approximate ones) and systematically produced numerical findings are summarized • The modulational instability in these models and its nonlinear development is addressed in detail • Stability and motion of multi-component solitons in binary and spinor (triple) solitons is considered

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“…In a general system, the localized waves are spatially, temporally (solitons and breathers) or spatiotemporally (RWs) localized, and will arise from vanishing or nonvanishing backgrounds, however, these solutions may also exhibit non-localized phenomena, or appear in a variable background height in some special systems, e.g. nonautonomous systems [44,45]. Considering the Gross-Pitaevskii equation (GPE) as [7] ih…”

Section: Introductionmentioning

confidence: 99%

Localized waves and mixed interaction solutions with dynamical analysis to the Gross–Pitaevskii equation in the Bose–Einstein condensate

et al. 2021

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We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

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Non-autonomous solitons in inhomogeneous nonlinear media with distributed dispersion

Cited by 37 publications

References 72 publications

Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

Spatiotemporal engineering of matter-wave solitons in Bose–Einstein condensates

Localized waves and mixed interaction solutions with dynamical analysis to the Gross–Pitaevskii equation in the Bose–Einstein condensate

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