On global behavior for complex soliton solutions of the perturbed nonlinear Schrödinger equation in nonlinear optical fibers

Osman, M. S.; Almusawa, Hassan; Tariq, Kalim U.; Anwar, Sadia; Kumar, Sachin; Younis, Muhammad; Ma, Wen‐Xiu

doi:10.1016/j.joes.2021.09.018

Cited by 43 publications

(6 citation statements)

References 78 publications

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“…It is also helpful in problem of optical pulse propagation in asymmetric, twin core optical fibers etc. Optical solitons, which are one of the most important solutions of nonlinear Schrodinger equation, are used in optical fiber communication [ 44 , 48 , 64 , 65 , 66 , 67 , 68 , 69 ].…”

Section: Nonlinear Evolutionary Equations and Their Examplesmentioning

confidence: 99%

Soliton: A dispersion-less solution with existence and its types

Arora

Rani

Emadifar

2022

Heliyon

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Section: Nonlinear Evolutionary Equations and Their Examplesmentioning

confidence: 99%

Soliton: A dispersion-less solution with existence and its types

Arora

Rani

Emadifar

2022

Heliyon

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“…The traveling wave solutions of the Boussinesq and Korteweg de Vries equations, which describe water waves, are well-known examples. For more information, see [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration

et al. 2023

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The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics.

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“…Before Russell's work was proven in the 1870s, prominent philosophers and scientists widely praised its scientific implications. Nonetheless, Rayleigh and Boussinesq's work demonstrates the critical issue of non-linearity and dispersion, It is still rendering to address Stokes and Airy's argument against using kink-shaped and bell-shaped solutions to simulate wave phenomena in the optical fibre, the elastic media and other important fields, well-known examples include the travelling wave solutions of Korteweg de Vries and the Boussinesq equation [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

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In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

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On global behavior for complex soliton solutions of the perturbed nonlinear Schrödinger equation in nonlinear optical fibers

Cited by 43 publications

References 78 publications

Soliton: A dispersion-less solution with existence and its types

Soliton: A dispersion-less solution with existence and its types

Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

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