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

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.

Dynamics of new optical solitons for the Triki–Biswas model using beta-time derivative

2021 ◽  
Author(s):  
Asim Zafar ◽  
Ahmet Bekir ◽  
M. Raheel ◽  
Kottakkaran Sooppy Nisar ◽  
Salman Mustafa
Keyword(s):  
Model Equation ◽  
Pulse Propagation ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Integration Schemes ◽  
Ultrashort Pulse Propagation ◽  
Different Types ◽  
Efficient Integration ◽  
Derivative Nonlinear Schrödinger Equation

This paper comprises the different types of optical soliton solutions of an important Triki–Biswas model equation with beta-time derivative. The beta derivative is considered as a generalized version of the classical derivative. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation that describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel beta derivative operator and three efficient integration schemes. During this work, a sequence of new optical solitons is produced that may have an importance in optical fiber systems. These solutions are verified and numerically simulated through soft computation.

New optical soliton solutions for Triki–Biswas model by new extended direct algebraic method

2020 ◽  
pp. 2150023
Author(s):  
Hadi Rezazadeh ◽  
Jamilu Sabi’u ◽  
Rajarama Mohan Jena ◽  
S. Chakraverty
Keyword(s):  
Optical Fiber ◽  
Group Velocity ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Algebraic Approach ◽  
Ultrashort Pulses ◽  
Algebraic Method ◽  
Optical Soliton

The study focuses on the use of a direct algebraic approach to the analysis of the Triki–Biswas (TB) model. This model addresses the distribution of ultrashort pulses in optical fiber in the presence of non-Kerr dispersion concept and group velocity dispersion. However, using the new extended direct algebraic method, we have obtained various optical soliton solutions for the TB model. The optical soliton solutions are new and reliable compared to the existing methods.

Highly dispersive optical soliton perturbation of Kudryashov’s arbitrary form having sextic-power law refractive index

2021 ◽  
Vol 35 (24) ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El-Barkouky ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
Rabab M. I. El-Hassani ◽  
...  
Keyword(s):  
Refractive Index ◽  
Power Law ◽  
Soliton Solutions ◽  
Research Paper ◽  
Optical Soliton ◽  
Integration Scheme ◽  
Arbitrary Form ◽  
Soliton Perturbation ◽  
Singular Soliton ◽  
Simple Integration

In this research paper, a simple integration scheme is executed to secure new dark and singular soliton solutions for the highly dispersive nonlinear Schrödinger’s equation having Kudryashov’s arbitrary form with generalized nonlocal laws and sextic-power law refractive index.

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

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.

Soliton interactions and modulation instability for the N-coupled complex short pulse equations in an optical fiber

2018 ◽  
Vol 32 (22) ◽  
pp. 1850252
Author(s):  
Yu-Feng Wang ◽  
Bo-Ling Guo
Keyword(s):  
Bound States ◽  
Mixed Type ◽  
Modulation Instability ◽  
Short Pulse ◽  
Soliton Solutions ◽  
Ultrashort Pulses ◽  
Soliton Interactions ◽  
Dark Solitons ◽  
Wave Solutions ◽  
Nonlinear Fiber

Under investigation in this paper are the N-coupled complex short pulse (N-CSP) equations, which describe the propagation of simultaneous N ultrashort pulses in a nonlinear fiber medium. Through the Hirota method, the m-bright-n-dark [Formula: see text] soliton solutions are obtained. Elastic and inelastic interactions between the mixed-type solitons are derived through the asymptotic analysis. As an example, the oblique interactions and the bound states of the 2-bright-1-dark and 1-bright-2-dark solitons for 3-CSP equations are analyzed graphically. Finally, the condition of the modulation instability of the plane-wave solutions for 2-CSP equations is given through the linear stability analysis.

scholarly journals Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

2018 ◽  
Vol 24 (1) ◽  
pp. 20-33 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Integration Scheme ◽  
Instability Analysis ◽  
Nonlinear Schrödinger

This paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrödinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE.

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