Analytical solutions for the variational equations derived for the nonlinear Schrödinger equation: Dispersion-managed fiber system

Abdosllam Moftah Abobaker; A.B. Moubissi; Th.B. Ekogo; Kaliyaperumal Nakkeeran

doi:10.1142/S0218863508004226

Analytical solutions for the variational equations derived for the nonlinear Schrödinger equation: Dispersion-managed fiber system

Abdosllam Moftah Abobaker, A.B. Moubissi, Th.B. Ekogo, Kaliyaperumal Nakkeeran

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider the nonlinear Schrödinger equation which governs
the pulse propagation in dispersion-managed (DM) optical fiber
transmission systems. Using a generalized form of ansatz function
for the shape of the pulse we derive the variational equations.
For a particular case of DM fiber system when the Hamiltonian is zero,
we solve the variational equations analytically and obtain
the expressions for the pulse energy, amplitude, width and chirp.
Finally for Gaussian and hyperbolic secant shaped pulses we show
through numerical simulations that the analytically calculated energy
(for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

Original language	English
Pages (from-to)	285-297
Number of pages	13
Journal	Journal of Nonlinear Optical Physics and Materials
Volume	17
Issue number	3
DOIs	https://doi.org/10.1142/S0218863508004226
Publication status	Published - Sept 2008

Keywords

Optical fibers
dispersion-managed (DM) solitons
nonlinear Schrödinger equation (NLSE)
variational method
Gaussian ansatz
hyperbolic secant ansatz

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10.1142/S0218863508004226

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@article{407291e4bc934522b01ae2a47b145e3b,

title = "Analytical solutions for the variational equations derived for the nonlinear Schr{\"o}dinger equation: Dispersion-managed fiber system",

abstract = "We consider the nonlinear Schr{\"o}dinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse we derive the variational equations. For a particular case of DM fiber system when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.",

keywords = "Optical fibers, dispersion-managed (DM) solitons, nonlinear Schr{\"o}dinger equation (NLSE), variational method, Gaussian ansatz, hyperbolic secant ansatz",

author = "Abobaker, {Abdosllam Moftah} and A.B. Moubissi and Th.B. Ekogo and Kaliyaperumal Nakkeeran",

year = "2008",

month = sep,

doi = "10.1142/S0218863508004226",

language = "English",

volume = "17",

pages = "285--297",

journal = "Journal of Nonlinear Optical Physics and Materials",

issn = "0218-8635",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

TY - JOUR

T1 - Analytical solutions for the variational equations derived for the nonlinear Schrödinger equation

T2 - Dispersion-managed fiber system

AU - Abobaker, Abdosllam Moftah

AU - Moubissi, A.B.

AU - Ekogo, Th.B.

AU - Nakkeeran, Kaliyaperumal

PY - 2008/9

Y1 - 2008/9

N2 - We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse we derive the variational equations. For a particular case of DM fiber system when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

AB - We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse we derive the variational equations. For a particular case of DM fiber system when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

KW - Optical fibers

KW - dispersion-managed (DM) solitons

KW - nonlinear Schrödinger equation (NLSE)

KW - variational method

KW - Gaussian ansatz

KW - hyperbolic secant ansatz

U2 - 10.1142/S0218863508004226

DO - 10.1142/S0218863508004226

M3 - Article

SN - 0218-8635

VL - 17

SP - 285

EP - 297

JO - Journal of Nonlinear Optical Physics and Materials

JF - Journal of Nonlinear Optical Physics and Materials

IS - 3

ER -

Analytical solutions for the variational equations derived for the nonlinear Schrödinger equation: Dispersion-managed fiber system

Abstract

Keywords

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