Nonlinear dispersive wave propagation pattern in optical fiber system

Uddin, M. Hafiz; Zaman, U.H.M.; Arefin, Mohammad Asif; Akbar, M. Ali

doi:10.1016/j.chaos.2022.112596

Cited by 24 publications

(5 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Substituting equation (7) and equation (8) into transformed ODE and putting the coefficients of W j to equal zero. This generates a system of equations.…”

Section: Methods IImentioning

confidence: 99%

“…They play a crucial role in elucidating intricate physical phenomena across diverse fields of physics including fluid dynamics, plasma, statistical, quantum, solid state, optical dynamics, and more [1][2][3][4][5]. Some special system of such equations in the study of transmission lines, optical fibers, and quantum mechanics have important applications [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

Raza,

Arshed,

Ali Shah

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

This article deals with a new version of the generalized Q-deformedSinh-Gordon equation. Numerous physical interpretations and applications exist for the said model in several scientific fields. Therefore, in order to obtain a better understanding of the underlying physical system, it is imperative to look at the traveling wave behavior displayed by this equation. To complete our thrust three innovative integration architectures including the modified sub-equation method, the $G'/(bG'+G+a)$-expansion method and $\frac{G'}{G^{2}}$-expansion method have been utilized to createprecise closed form traveling wave solutions. These methods provide solutions in the form of hyperbolic function solutions, trigonometric function solutions and rational solutions. The obtained solutions are discussed with $3D$ surface plots and $2D$line plots to visualize and support the theoretical results. Furthermore, stability analysis of the proposed model is also carried out. This paper discusses a major development as well as gradual improvements to previous works on the current model. Moreover, we discuss the stability analysis of the studied equation and the outcomes are visually depicted in graphical form. To authenticate the solutions provided in this manuscript, each solution undergoes a meticulous validation process by reintegrating it into the original model using computational software.

show abstract

“…Substituting equation (7) and equation (8) into transformed ODE and putting the coefficients of W j to equal zero. This generates a system of equations.…”

Section: Methods IImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

Raza,

Arshed,

Ali Shah

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…As shown in Figure 1. If the initial pulse has the proper form, nonlinear processes can accurately cancel dispersion, producing a pulse with a consistent shape that defined a soliton [1,5]. While there are a number of partially differential nonlinear dispersive formulae that provide soliton solutions, the Schrodinger nonlinear equation which describes the waves of light in fiber optics more crucially is the most essential one (among those that characterize physical systems) [1,6], Since a soliton is a constant wave that is both confined (although they were moving) and capable of intense interaction with other solitons while maintaining its identity, it is generally understood to refer to any solution of a nonlinear equation [7].…”

Section: Introductionmentioning

confidence: 99%

Optimize Nonlinear Effects on Fundamental and High-order Soliton in Photonic Crystal Fiber

Jasim AL-Taie,

Matrood

2024

Mal. J. Fund. Appl. Sci.

View full text Add to dashboard Cite

Nonlinear effects in optical fibers are mainly caused by two sources: inelastic scattering behaviour or the intensity sensitivity of the medium's refractive index. The propagation process in photonic crystal fibers is more complex than the propagation process of first-order solitons, second-order solitons, and third-order solitons. This article discusses the effects of propagation on first-, second- and third-order solitons. A popular approach to supercontinuum generation through soliton fission is the higher-order soliton technique for spectral generation.

show abstract

“…There are many important NLPDEs such as Hopf equation modeling the dynamics of gases (Bogomolov and Kuvshinnikov, 2019), Rosenau–Hyman equation emerging in the creation of patterns in liquid droplets (Cinar et al ., 2021a), Burgers equation modeling acoustic and hydrodynamic waves (Tamang and Saha, 2020), Fisher equation (Secer and Cinar, 2020) used in heat transfer and ecology, Schrödinger equations (Sulaiman and Bulut, 2020; Ozdemir et al ., 2021; Cinar et al ., 2021b; Esen et al ., 2021) and their variants frequently used in optics and superconductivity (Cinar et al ., 2021b; Onder et al ., 2022a), Korteveg de Vries and variant equations, which are commonly used in mechanics and water waves (Johnson, 1980), Kadomtsev Petviashvili-modified equal width (MEW) equation (Islam et al. , n.d; Islam et al ., 2022a), nonlinear time fractional Klein–Gordon and Sine-Gordon equations (Uddin et al ., 2022; Sadiya et al ., 2022), space-time-fractional coupled Whitham–Broer–Kaup (WBK) and coupled approximate long water (ALW) wave equations (Zaman et al ., 2022), nonlinear Schrödinger equation (Islam et al ., 2022b), Sasa–Satsuma model (Ozdemir et al ., 2022; Cinar et al ., 2022), Fokas–Lenells and Schrödinger–Hirota equations (Ozisik et al ., 2023), Wazwaz–Benjamin–Bona–Mahony equations (Onder et al ., 2022b), nonlinear refractive index cubic-quartic equation (Batool et al ., 2022) and Boussinesq equation used in modeling water waves (Schäffer et al ., 1993).…”

Section: Introductionmentioning

confidence: 99%

On soliton solutions of the modified equal width equation

Onder

Çinar

Seçer

et al. 2023

View full text Add to dashboard Cite

PurposeThe soliton solutions are obtained by using extended rational sin/cos and sinh-cosh method. The methods are powerful and have ease of use. Applying wave transformation to the nonlinear partial differential equations (NLPDEs) and the considered equation turns into a nonlinear differential equation (NODE). According to the methods, the solution sets of the NODE are supposed to the form of the rational terms as sinh/cosh and sin/cos and the trial solutions are substituted into the NODE. Collecting the same power of the trigonometric functions, a set of algebraic equations is derived.Design/methodology/approachThe main purpose of this paper is to obtain soliton solutions of the modified equal width (MEW) equation. MEW is a form of regularized-long-wave (RLW) equation that represents one-dimensional wave propagation in nonlinear media with dispersion processes. This is also used to simulate the undular bore in a long shallow water canal.FindingsThus, the solution of the main PDE is reduced to the solution of a set of algebraic equations. In this paper, the kink, singular and singular periodic solitons have been successfully obtained.Originality/valueIllustrative plots of the solutions have been presented for physical interpretation of the obtained solutions. The methods are powerful and might be used to solve a broad class of differential equations in real-life problems.

show abstract

Nonlinear dispersive wave propagation pattern in optical fiber system

Cited by 24 publications

References 30 publications

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

Optimize Nonlinear Effects on Fundamental and High-order Soliton in Photonic Crystal Fiber

On soliton solutions of the modified equal width equation

Contact Info

Product

Resources

About