On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation

Rehman, Shafiq Ur; Seadawy, Aly R.; Younis, Muhammad; Rizvi, Syed T. R.

doi:10.1007/s11082-021-03028-1

Cited by 20 publications

(2 citation statements)

References 41 publications

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“…To unravel the mysteries of nature's nonlinearities, it is crucial to find exact solutions to these equations. Fortunately, numerous effective methods have been devised for constructing exact solutions to nonlinear partial differential equations [1][2][3][4]. These methods yield a diverse array of solitary wave solutions, including kink-type waves, lump solutions, breather solutions, periodic solitary waves, and many others [5,6].…”

Section: Introductionmentioning

confidence: 99%

Exact soliton solutions and soliton diffusion of two kinds of stochastic KdV equations with variable coefficients

Wang,

Li,

Wang

et al. 2023

Phys. Scr.

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In this paper, we consider the exact solutions and soliton diffusion phenomenon of two kinds of stochastic KdV equations with variable coefficients. Firstly, according to symmetric reduction, stochastic KdV equations with variable coefficients are transformed into a coupled system of a deterministic KdV-type equation with variable coefficients and a solvable stochastic ordinary differential equation. Then, by the generalized wave transformation and the Clarkson-Kruskal direct method, we obtain the exact solutions of the deterministic KdV-type equation with variable coefficients. By coupling with the exact solutions of the stochastic ordinary differential equation, the exact solutions of stochastic KdV equations with variable coefficients are obtained. Compared to Wick-type stochastic KdV equations, our research work does not require additional inverse transformations, but solves stochastic partial differential equations more concisely, systematically, and directly. Secondly, two examples are given to verify the correctness of the theoretical analysis, and the soliton diffusion phenomenon of the system is discussed. Finally, by the Zabusky-Kruskal finite difference scheme, numerical simulations are provided to demonstrate the effectiveness of the analytic methods. The results indicate that the soliton diffusion phenomenon is subject to noise influence. In particular, the wave speed accelerates the soliton diffusion over time in the multiplicative noise background, and the wave speed slows down the soliton diffusion over time in the additive noise background.

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Section: Introductionmentioning

confidence: 99%

Exact soliton solutions and soliton diffusion of two kinds of stochastic KdV equations with variable coefficients

Wang,

Li,

Wang

et al. 2023

Phys. Scr.

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show abstract

“…A new fractional derivative with a nonsingular kernel involving exponential, Mittag-leffler, power functions, and some advanced approaches for epidemic models have been elaborated in [8,11,27,27,28,30]. The Lie group method is used in [32] to obtain the Lie symmetry algebra admitted by the time fractional Black-Scholes equation. In [12], authors build a proper extension of the classical prolongation formula of conformable derivative point transformations.…”

Section: Introductionmentioning

confidence: 99%

Computer Virus Fractional Order Model with Effects of Internal and External Storage Media

Farman¹,

Akgül²,

Shanak³

et al. 2022

Eur. J. Pure Appl. Math.

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In this work, we focus on the implementation of epidemic techniques on computer virus and study the dynamic transmission of several viruses to minimize the destruction of computers. We aim to make and analyze computer viruses through the Atangana-Baleanu sense and the Atangana-Taufik scheme, which is used for the fractional derivative model for the computer virusepidemic. It contained infected external computer effects and removable storage media on the computer viruses. For the validation of the model, we also discussed its positivity and boundedness. Fixed point theory and the iterative methods helped a lot to find out the existence and uniqueness of the model. In the case of numerical simulation, we used Atanagana-Taufik technique to illustratethe effects of varying the fractional order. The graphical results support our theoretical results from which, we analyze the infected external computer effects and removable storage media on the computer viruses.

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Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

Chen

2024

Math Methods in App Sciences

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In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov's with sextic‐power law refractive index and generalized nonlocal laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell‐shaped soliton solutions, and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model's solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.

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On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation

Cited by 20 publications

References 41 publications

Exact soliton solutions and soliton diffusion of two kinds of stochastic KdV equations with variable coefficients

Exact soliton solutions and soliton diffusion of two kinds of stochastic KdV equations with variable coefficients

Computer Virus Fractional Order Model with Effects of Internal and External Storage Media

Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

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