Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Ahmed, Hamdy M.; Rabie, Wafaa B.

doi:10.1007/s11082-021-03026-3

Cited by 38 publications

(3 citation statements)

References 43 publications

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“…Finding an analytical solution to differential equations is accomplished using the extended direct algebraic method. Some recent works on the analytical solutions of nonlinear PDEs are done in [38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Fatima,

Abbas,

Muhammad

2023

Phys. Scr.

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The present investigation describes the dynamical behavior, multi-stability, and traveling wave solutions of thin-film polarisation equations (TFPE) which describes the propagation of waves in thin-film ferroelectric materials. The extended direct algebraic technique is used to construct the traveling wave patterns. Visual representations of a few randomly selected solutions are provided for physical comprehension. The ordinary differential equation can be expressed in the planar dynamical system using the Galilean transformation. Using various initial conditions for the unperturbed dynamical system, phase portraits with various sorts of trajectories are created. Additionally, the Runge-Kutta method is used to plot nonlinear periodic waves and super nonlinear waves. Additionally, the Hamiltonian function for this undisturbed dynamical system is computed and shown. It also included the source term with amplitude and frequency parameters for the chaotic and quasi-periodic behaviors, and the system is also stated in the non-autonomous form. For the dynamical system under investigation, multi-stability is also thoroughly described. Furthermore, a full inspection of the sensitivity of the perturbed dynamical structure under various initial conditions has been conducted.

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Section: Introductionmentioning

confidence: 99%

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Fatima,

Abbas,

Muhammad

2023

Phys. Scr.

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show abstract

“…Nevertheless, as the literature indicates, discovering these answers has not been simple. In recent studies [27][28][29][30][31][32][33], the research scholars provided a straightforward method for constructing travelling wave solutions to general nonlinear equations, which may or may not be integrable, beginning with solutions of simple equations (including even linear equations). As proved by nontrivial examples (usually involving equations of the third order), this method is particularly effective for getting travelling wave solutions of nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Travelling Wave Solutions of the Non-Linear Wave Equations

Haider

Gul

Rahman

et al. 2023

Acta Mechanica Et Automatica

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This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. The periodic solutions are found using this method which contains both solitary wave and shock wave solutions. In this paper, the new results are computed using the closed-form solution including solitary or shock wave solutions which are obtained using Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised and the periodic behaviour of the solution is described in detail. The shock waves are found to break with time, whereas, solitary waves are found to be improved continuously with time.

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“…In the single-mode fiber, the picosecond optical pulse happens the symmetrical broadening of pulse time and frequency domains respectively due to the effects of group-velocity dispersion (GVD) and the self-phase modulation (SPM). When these two effects achieve a complete mutual balance, bright and dark solitons form in the abnormal and normal dispersion regions respectively [3,4]. When the pulse width reaches the order of femtosecond or subfemtosecond, the influence of various higher-order effects on the pulse can not be ignored [5,6].…”

Section: Introductionmentioning

confidence: 99%

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

Fang¹,

Bo²,

Wang³

et al. 2022

Chaos, Solitons & Fractals

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Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Cited by 38 publications

References 43 publications

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Travelling Wave Solutions of the Non-Linear Wave Equations

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

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