Soliton propagation along optical fibers

Ohkuma, Kenji; Ichikawa, Yasuaki; Abe, Yoshihiko

doi:10.1364/ol.12.000516

Cited by 91 publications

(37 citation statements)

References 13 publications

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“…19 • On the contrary, the same model plays a fundamental role in plasma physics. In warm multi-species plasmas with anisotropic pressures and different equilibrium drifts, coupled DNLSEs govern the oblique propagation of nonlinear magnetohydrodynamic waves relative to an external magnetic field under certain conditions, dropping the quasi-neutrality assumption [20].…”

Section: Gauge Transformations and Applicationsmentioning

confidence: 99%

“…Besides the technique of inverse scattering transform [15], the Hirota bilinear method is also applicable to these equations [17]. In addition to their great significance as examples of nonlinear dynamics in a general setting, these equations are also well known as relevant models for the properties of very narrow pulses in nonlinear optics [18,19], the propagation of Alfvén waves in magnetized plasmas [20,21], and the description of electromagnetic waves in an antiferromagnetic medium [22].…”

Section: Introductionmentioning

confidence: 99%

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Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

et al. 2016

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Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics and plasmas, exhibits RWs only in the regime of modulation instability (MI) of the background.For system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect will be demonstrated for a system of coupled derivative NLSEs (DNLSEs), where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs will depend on the mismatch in group velocities between the components, as well as the parameters for cubic nonlinearity and self-steepening. RWs considered in this work differ from those of the NLSEs in terms of the amplification ratio and criteria of existence.Applications to optics and plasma physics are discussed.3

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Section: Gauge Transformations and Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

et al. 2016

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“…Thereby we neglect terms like |ν 0 − ν j |ǫ and |µ 0 − µ j |ǫ which due to (15) and (18) are of the higher order in ǫ. Hence, eq.…”

Section: Derivation Of the Complex Toda Chain Modelmentioning

confidence: 99%

“…Moreover, we have to stress that it is the completely integrable model (1) that should be considered as a true starting point for analytical investigation of subpicosecond soliton dynamics. Indeed, it was shown in [15] that numerical simulation of the soliton propagation according to the MNSE (1) revealed various kinds of dynamical behavior which cannot be accounted for by treating the nonlinearity dispersion term of the MNSE (1) as a perturbation term in the NSE. Analogous idea in treating the perturbed NSE was developed by Kodama and Hasegawa in [16].…”

Section: Introductionmentioning

confidence: 99%

Adiabatic interaction ofNultrashort solitons: Universality of the complex Toda chain model

Gerdjikov

Yang

2001

Phys. Rev. E

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Using the Karpman-Solov'ev method we derive the equations for the 2-soliton adiabatic interaction for solitons of the modified nonlinear Schrödin-ger equation (MNSE). Then we generalize these equations to the case of N interacting solitons with almost equal velocities and widths. On the basis of this result we prove that the N MNSE-soliton train interaction (N > 2) can be modeled by the completely integrable complex Toda chain (CTC). This is an argument in favor of universality of the complex Toda chain which was previously shown to model the soliton train interaction for nonlinear Schrödinger solitons. The integrability of the CTC is used to describe all possible dynamical regimes of the N -soliton trains which include asymptotically free propagation of all N solitons, N -soliton bound states, various mixed regimes, etc. It allows also to describe analytically the manifolds in the 4N -dimensional space of initial soliton parameters which are responsible for each of the regimes mentioned above. We compare the results of the CTC model with the numerical solutions of the MNSE for 2 and 3-soliton interactions and find a very good agreement.

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“…Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. The derivative nonlinear Schrödinger (DNLS) equation is an integrable model describing various nonlinear waves such as nonlinear Alfvén waves in space plasma(see, e.g., [1,2,3,4,5,6,7]), sub-picosecond pulses in single mode optical fibers(see, e.g., [8,9,10,11,12]), and weak nonlinear electromagnetic waves in ferromagnetic [13], antiferromagnetic [14], and dielectric[15] systems under external magnetic fields. Both of vanishing boundary conditions (VBC) and nonvanishing boundary conditions (NVBC) for the DNLS equation are physically significant.…”

Section: Introductionmentioning

confidence: 99%

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Chen¹,

Yang²,

Lam³

2006

J. Phys. A: Math. Gen.

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An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. The derivative nonlinear Schrödinger (DNLS) equation is an integrable model describing various nonlinear waves such as nonlinear Alfvén waves in space plasma(see, e.g., [1,2,3,4,5,6,7]), sub-picosecond pulses in single mode optical fibers(see, e.g., [8,9,10,11,12]), and weak nonlinear electromagnetic waves in ferromagnetic [13], antiferromagnetic [14], and dielectric[15] systems under external magnetic fields. Both of vanishing boundary conditions (VBC) and nonvanishing boundary conditions (NVBC) for the DNLS equation are physically significant. For problems of nonlinear Alfvén waves, weak nonlinear electromagnetic waves in magnetic and dielectric media, waves propagating strictly parallel to the ambient magnetic fields are modelled by VBC while those oblique waves are modelled by NVBC. In optical fibers, pulses under bright background waves are modelled by NVBC.

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Soliton propagation along optical fibers

Cited by 91 publications

References 13 publications

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

Adiabatic interaction ofNultrashort solitons: Universality of the complex Toda chain model

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

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