Construction of Multi-soliton Solutions of the N-Coupled Hirota Equations in an Optical Fiber*

In this paper, under investigation is a (2 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation, which is introduced to the study of an optical fiber, where [Formula: see text] is the temporal variable, variable coefficients [Formula: see text] and [Formula: see text] are related to the group velocity dispersion, [Formula: see text] and [Formula: see text] represent the Kerr nonlinearity and linear term, respectively. Via the Hirota bilinear method, bilinear forms are obtained, and bright one-, two-, three- and N-soliton solutions as well as dark one- and two-soliton solutions are derived, where [Formula: see text] is a positive integer. Velocities and amplitudes of the bright/dark one solitons are obtained via the characteristic-line equations. With the graphical analysis, we investigate the influence of the variable coefficients on the propagation and interaction of the solitons. It is found that [Formula: see text] can only affect the phase shifts of the solitons, while [Formula: see text], [Formula: see text] and [Formula: see text] determine the amplitudes and velocities of the bright/dark solitons.

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Bilinear forms and dark-soliton solutions for a fifth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber

Modern Physics Letters B ◽

10.1142/s0217984916503127 ◽

2016 ◽

Vol 30 (24) ◽

pp. 1650312 ◽

Cited By ~ 14

Author(s):

Chen Zhao ◽

Yi-Tian Gao ◽

Zhong-Zhou Lan ◽

Jin-Wei Yang ◽

Chuan-Qi Su

Keyword(s):

Schrödinger Equation ◽

Optical Fiber ◽

Nonlinear Schrödinger Equation ◽

Variable Coefficient ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Bilinear Forms ◽

Order Variable ◽

Fifth Order

In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation is investigated, which describes the propagation of the attosecond pulses in an optical fiber. Via the Hirota’s method and auxiliary functions, bilinear forms and dark one-, two- and three-soliton solutions are obtained. Propagation and interaction of the solitons are discussed graphically: We observe that the solitonic velocities are only related to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the coefficients of the second-, third-, fourth- and fifth-order terms, respectively, with [Formula: see text] being the scaled distance, while the solitonic amplitudes are related to [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] as well as the wave number. When [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are the constants, or the linear, quadratic and trigonometric functions of [Formula: see text], we obtain the linear, parabolic, cubic and periodic dark solitons, respectively. Interactions between (among) the two (three) solitons are depicted, which can be regarded to be elastic because the solitonic amplitudes remain unchanged except for some phase shifts after each interaction in an optical fiber.

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Wave Behaviors of Kundu–Mukherjee–Naskar Model Arising In Optical Fiber Communication Systems with Complex Structure

10.21203/rs.3.rs-168692/v1 ◽

2021 ◽

Author(s):

Hadi Rezazadeh ◽

Ali Kurt ◽

Ali Tozar ◽

Orkun Tasbozan ◽

Seyed Mehdi Mirhosseini-Alizamini

Keyword(s):

Optical Fiber ◽

Communication Systems ◽

Complete Solution ◽

Complex Structure ◽

Soliton Solutions ◽

Optical Fiber Communication ◽

Rogue Waves ◽

Fiber Communication ◽

Soliton Dynamics ◽

Functional Variable Method

Abstract Rogue waves are very mysterious and extra ordinary waves. They appear suddenly even in a calm sea and are hard to be predicted. Although nonlinear Schrödinger equation (NLS) provides a perspective, it alone can neither detect rogue waves nor provide a complete solution to problems. Therefore, some approximations are still mandatory for both obtaining an exact solution and predicting rogue waves. Such as Kundu-Mukherjee-Naskar (KMN) model which allows obtaining lump-soliton solutions considered as rogue waves. In this study the functional variable method is utilized to obtain the analytical solutions of KMN model that corresponds to the propagation of soliton dynamics in optical fiber communication system.

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Solitary wave solutions of Kaup–Newell optical fiber model in mathematical physics and its modulation instability

Modern Physics Letters B ◽

10.1142/s0217984920502772 ◽

2020 ◽

Vol 34 (26) ◽

pp. 2050277

Author(s):

Muhammad Arshad ◽

Aly R. Seadawy ◽

Dianchen Lu ◽

Farhan Ali

Keyword(s):

Optical Fiber ◽

Modulation Instability ◽

Soliton Solutions ◽

Mathematical Physics ◽

Solitary Wave Solutions ◽

Trigonometric Functions ◽

Fiber Model ◽

Wave Solutions ◽

Long Wave ◽

Expansion Scheme

Soliton solutions which signify long wave parallel to the magnetic fields of Kaup–Newell optical fiber model are discussed in this paper by two different methods. The improved simple equation method (ISEM) and exp[Formula: see text]-expansion scheme are employed to solve the model to construct the solutions of the model in different cases. The achieved solutions are represented in different and general forms such as logarithmic or exponential function, trigonometric and hyperbolic trigonometric functions, etc. Also, the modulation instability of the model is analyzed which confirms that all obtained exact results are stable. Several solutions from achieved solutions are novel.

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Lax pair, Darboux transformation, vector rational and semi-rational rogue waves for the three-component coupled Hirota equations in an optical fiber

The European Physical Journal Plus ◽

10.1140/epjp/i2019-12515-4 ◽

2019 ◽

Vol 134 (5) ◽

Cited By ~ 6

Author(s):

Zhong Du ◽

Bo Tian ◽

Han-Peng Chai ◽

Xue-Hui Zhao

Keyword(s):

Optical Fiber ◽

Darboux Transformation ◽

Rogue Waves ◽

Lax Pair ◽

Transformation Vector ◽

Hirota Equations

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Propagation of diverse ultrashort pulses in optical fiber to Triki–Biswas equation and its modulation instability analysis

Modern Physics Letters B ◽

10.1142/s0217984921504911 ◽

2021 ◽

Author(s):

Tukur Abdulkadir Sulaiman ◽

Abdullahi Yusuf ◽

Bashir Yusuf ◽

Dumitru Baleanu

Keyword(s):

Optical Fiber ◽

Model Equation ◽

Pulse Propagation ◽

Modulation Instability ◽

Soliton Solutions ◽

Ultrashort Pulses ◽

Optical Soliton ◽

Integration Scheme ◽

Efficient Integration ◽

Complex Models

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations.

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Stochastic Soliton Solutions of the High-Order Nonlinear Schrödinger Equation in the Optical Fiber with Stochastic Dispersion and Nonlinearity

Zeitschrift für Naturforschung A ◽

10.5560/zna.2013-0071 ◽

2014 ◽

Vol 69 (1-2) ◽

pp. 21-33 ◽

Cited By ~ 1

Author(s):

Hui Zhong ◽

Bo Tian

Keyword(s):

Optical Fiber ◽

White Noise ◽

Gaussian White Noise ◽

Soliton Solutions ◽

Periodic Oscillation ◽

Bound State ◽

High Order ◽

Soliton Propagation ◽

Nonlinear Schrödinger ◽

White Noise Functional

In this paper, the high-order nonlinear Schrödinger (HNLS) equation driven by the Gaussian white noise, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is studied. With the white noise functional approach and symbolic computation, stochastic one- and two-soliton solutions for the stochastic HNLS equation are obtained. For the stochastic one soliton, the energy and shape keep unchanged along the soliton propagation, but the velocity and phase shift change randomly because of the effects of Gaussian white noise. Ranges of the changes increase with the increase in the intensity of Gaussian white noise, and the direction of velocity is inverted along the soliton propagation. For the stochastic two solitons, the effects of Gaussian white noise on the interactions in the bound and unbound states are discussed: In the bound state, periodic oscillation of the two solitons is broken because of the existence of the Gaussian white noise, and the oscillation of stochastic two solitons forms randomly. In the unbound state, interaction of the stochastic two solitons happens twice because of the Gaussian white noise. With the increase in the intensity of Gaussian white noise, the region of the interaction enlarges.

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