Properties of soliton solutions on a cw background in optical fibers with higher-order effects

We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly.We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons

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Noncommutative coupled complex modified Korteweg–de Vries equation: Darboux and binary Darboux transformations

Modern Physics Letters A ◽

10.1142/s0217732319500548 ◽

2019 ◽

Vol 34 (07n08) ◽

pp. 1950054

Author(s):

H. Wajahat A. Riaz

Keyword(s):

Evolution Equations ◽

Nonlinear Evolution ◽

Vries Equation ◽

Soliton Solutions ◽

Higher Order ◽

Nonlinear Evolution Equations ◽

Order Effects ◽

Darboux Transformations ◽

De Vries ◽

Higher Order Effects

Higher-order nonlinear evolution equations are important for describing the wave propagation of second- and higher-order number of fields in optical fiber systems with higher-order effects. One of these equations is the coupled complex modified Korteweg–de Vries (ccmKdV) equation. In this paper, we study noncommutative (nc) generalization of ccmKdV equation. We present Darboux and binary Darboux transformations (DTs) for the nc-ccmKdV equation and then construct its Quasi-Grammian solutions. Further, single and double-hump soliton solutions of first- and second-order are given in commutative settings.

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Femtosecond pulse propagation in optical fibers: higher order effects

IEEE Journal of Quantum Electronics ◽

10.1109/3.133 ◽

1988 ◽

Vol 24 (2) ◽

pp. 365-372 ◽

Cited By ~ 31

Author(s):

W. Zhao ◽

E. Bourkoff

Keyword(s):

Optical Fibers ◽

Femtosecond Pulse ◽

Pulse Propagation ◽

Higher Order ◽

Order Effects ◽

Higher Order Effects

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DARK SOLITONS IN OPTICAL FIBERS WITH HIGHER ORDER EFFECTS

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863502000985 ◽

2002 ◽

Vol 11 (02) ◽

pp. 197-204 ◽

Cited By ~ 1

Author(s):

K. NAKKEERAN

Keyword(s):

Optical Fibers ◽

Dark Soliton ◽

Higher Order ◽

Order Effects ◽

Nonlinear Wave Propagation ◽

Bilinear Method ◽

Fiber System ◽

Normal Dispersion ◽

Dispersion Regime ◽

Higher Order Effects

We consider the higher order nonlinear Schrödinger (HNLS) equation, which governs the nonlinear wave propagation in optical fibers with higher order effects. Lax pair associated with the integrable HNLS equation for the pulse propagation in normal dispersion regime of the fiber media is constructed with the help of Ablowitz–Kaup–Newell–Segur method. Using Hirota bilinear method, dark soliton solution is explicitly derived. Similar study is also carried out for simultaneous propagation of N nonlinear pulses in the normal dispersion regime of the fiber system with higher order effects.

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