Solitary waves travelling along an unsmooth boundary

He, Ji‐Huan; Qie, Na; He, Chun‐Hui

doi:10.1016/j.rinp.2021.104104

Cited by 119 publications

(43 citation statements)

References 41 publications

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“…e compliant fractional derivative of Atangana is used here on the grounds of its supremacy over other concepts of fractional derivatives [14,15]. is superiority is apparent in its capacity to extend all organizational characteristics, such as a chain law, quotient law, semigroup property, and element rule, to the traditional first derivative [16,17].…”

Section: Introductionmentioning

confidence: 99%

Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation

Khater

Inc

Attia

et al. 2022

Advances in Mathematical Physics

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This research paper explores the Atangana conformable nonlinear fractional Schrödinger equation’s optical soliton wave solutions through three recently introduced computational schemes. The simplest expanded equation, the generalized Kudryashov method, and the sech-tanh expansion approaches are used for describing the structure of optical solitons by nonlinear optical fibers with the modern fractional operator. Several formulas such as hyperbolic, trigonometric, logical, dim, light, moon-bright hybrid, singular, combined singular, and regular wave solutions have been created. The employed methods are effective and worthy of being tested. The features of the Hamiltonian process were used to analyze the stability properties of the solutions obtained.

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Section: Introductionmentioning

confidence: 99%

Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation

Khater

Inc

Attia

et al. 2022

Advances in Mathematical Physics

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“…The homotopy perturbation method [4][5][6][7][8][9][10][11]15,[24][25][26][27]43,44,47,55] constructs an effective iteration algorithm by guaranteeing its iteration path from the initial guess to the exact solution. The variational iteration method [29,32,35,51] adopts the variational theory [33,34] to find an optimal iteration formulation for differential equations. Taylor's series method [20,23] is simple, but only an infinite series solution is useful for analysis of a complex nonlinear problem.…”

Section: Introductionmentioning

confidence: 99%

New optimal fourth-order iterative method based on linear combination technique

Nadeem

Ali

2021

Hacettepe Journal of Mathematics and Statistics

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Newton's iteration method is widely used in numerical methods, but its convergence is low. Though a higher order iteration algorithm leads to a fast convergence, it is always complex. An optimal iteration formulation is much needed for both fast convergence and simple calculation. Here, we develop a two-step optimal fourth-order iterative method based on linear combination of two iterative schemes for nonlinear equations, and we explore the convergence criteria of the proposed method and also demonstrate its validity and efficiency by considering some test problems. We present both numerical as well as graphical comparisons. Further, the dynamical behavior of the proposed method is revealed.

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“…14 Now, the formulation has been extended to fractal oscillators with great success. [15][16][17][18][19] In this paper, we will consider a nonlinear oscillator with zero conditions. [18][19][20][21][22][23][24][25][26] Zero initial condition oscillator Instead of equation ( 1), we consider the following nonlinear oscillator with zero initial conditions…”

Section: Introductionmentioning

confidence: 99%

A fast estimation of the frequency property of the microelectromechanical system oscillator

Zhang

Tian

Pang

2021

Journal of Low Frequency Noise, Vibration and Active Control

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A nonlinear oscillator with zero initial conditions is considered, which makes some effective methods, for example, the variational iteration method and the homotopy perturbation method, invalid. To solve the bottleneck, this paper suggests a simple transform to convert the problem into a traditional case so that He’s frequency formulation can be effectively used to solve its approximate solution. An microelectromechanical system (MEMS) oscillator is used as example to show the solution process, and a good result is obtained.

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Solitary waves travelling along an unsmooth boundary

Cited by 119 publications

References 41 publications

Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation

Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation

New optimal fourth-order iterative method based on linear combination technique

A fast estimation of the frequency property of the microelectromechanical system oscillator

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