Multi-Soliton Solutions of a Coupled System of the Nonlinear Schrödinger Equation and the Maxwell-Bloch Equations

Kakei, Saburo; Satsuma, Junkichi

doi:10.1143/jpsj.63.885

Cited by 51 publications

(60 citation statements)

References 11 publications

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“…Further, Kakei and Satsuma [7] also reported the Lax pair and the multi-soliton solution of the NLS-MB equations. The integrability aspects of NLS-MB system with variable dispersion, the study of propagation of optical solitons in coupled NLS-MB, and random nonuniform-doped media have been reported earlier wherein the spectral parameter was kept constant.…”

Section: Introductionmentioning

confidence: 94%

Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

He¹,

Xu²,

Porsezian³

2013

Phys. Rev. E

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The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope E, polarization p and population inversion η. The norder breather solutions of the three fields are constructed using Darboux transformation (DT) by assuming periodic seed solutions. What is more, the n-order rogue waves are given by determinant forms with n + 3 free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.

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Section: Introductionmentioning

confidence: 94%

Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

He¹,

Xu²,

Porsezian³

2013

Phys. Rev. E

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“…Here in order to study multi-peak solitons on the planewave background (2) in the H-MB model, we shall keep a, k = 0. On the other hand, we pay our attention to multi-peak structures in electric field, i.e., the pulse propagation in the E component.…”

Section: The H-mb System and Exact Multi-peak Soliton Solutionmentioning

confidence: 99%

“…Nonlinear waves propagating in an erbium-doped fiber system have attracted special attention, since the resonant absorption of the erbium-doped two levels system is a good solution to the optical losses [1][2][3][4][5][6][7][8][9]. One of the most well-known examples is the amplification and reshaping of optical soltion (bright soliton on a zero background) in a long-haul optical communication through fibers with an active region doped with erbium atoms.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, nonlinear wave propagation could possess both the effects due to a mix of silica and erbium impurities. More specifically, the silica material gives the group velocity dispersion and self-phase modulation effects, which is governed by the nonlinear Schrödinger (NLS) equation; whereas Er impurities contribute to the self-induced transparency (SIT), which is described by the Maxwell-Bloch (MB) model [1][2][3][4][5][6][7][8][9]. As a result, the constraint to the NLS soliton namely the optical losses can be somewhat compensated with the effect of SIT.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, the constraint to the NLS soliton namely the optical losses can be somewhat compensated with the effect of SIT. In general, the dynamics of these waves in the erbium-doped fibers is described by the coupled system of the NLS and the MB equations [1][2][3][4]. It should be emphasized that recent experiments have confirmed guided wave SIT soliton formation and propagation by employing a few meters of erbium-doped fiber [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system

et al. 2016

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We study multi-peak solitons on a plane-wave background in an erbium-doped fiber system with some higher-order effects, which is governed by a coupled Hirota and Maxwel-Bloch (H-MB) model. The important characteristics of multi-peak solitons induced by the higher-order effects, such as the velocity changes, localization or periodicity attenuation, and state transitions, are revealed in detail. In particular, our results demonstrate explicitly that a multi-peak soliton can be converted to an antidark soliton when the periodicity vanishes; on the other hand, a multi-peak soliton is transformed to a periodic wave when the localization vanishes. Numerical simulations are performed to confirm the propagation stability of multi-peak solitons riding on a plane-wave background. Finally, we compare and discuss the similarity and difference of multi-peak solitons in special degenerate cases of the H-MB system with general existence conditions.

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Nonlinear Waves in Optical Waveguides and Soliton Theory Applications

Leble

2002

Optical Solitons

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Multi-Soliton Solutions of a Coupled System of the Nonlinear Schrödinger Equation and the Maxwell-Bloch Equations

Cited by 51 publications

References 11 publications

Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system

Nonlinear Waves in Optical Waveguides and Soliton Theory Applications

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