Solution of Sakata-Taketani Equation via the Caputo and Riemann-Liouville Fractional Derivatives

Merad, Hadjer; Merghadi, Faycel; Merad, Ahcene

doi:10.1016/s0034-4877(22)00038-6

Reports on Mathematical Physics

2022

DOI: 10.1016/s0034-4877(22)00038-6

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Solution of Sakata-Taketani Equation via the Caputo and Riemann-Liouville Fractional Derivatives

Hadjer Merad

Faycel Merghadi

Ahcene Merad

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Cited by 2 publications

References 17 publications

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Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

Riaz,

Jhangeer,

Martinovic

et al. 2024

Nonlinear Engineering

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Shallow water waves represent a significant and extensively employed wave type in coastal regions. The unconventional bidirectional transmission of extended waves across shallow water is elucidated through nonlinear fractional partial differential equations, specifically the space–time fractional-coupled Whitham–Broer–Kaup equation. The application of two distinct analytical methods, namely, the generalized logistic equation approach and unified approach, is employed to construct various solutions such as bright solitons, singular solitary waves, kink solitons, and dark solitons for the proposed equation. The physical behavior of calculated results is graphically represented through density, two- and three-dimensional plots. The obtained solutions could have significant implications across a range of fields including plasma physics, biology, quantum computing, fluid dynamics, optics, communication technology, hydrodynamics, environmental sciences, and ocean engineering. Furthermore, the qualitative assessment of the unperturbed planar system is conducted through the utilization of bifurcation theory. Subsequently, the model undergoes the introduction of an outward force with the aim of inducing disruption, resulting in the emergence of a perturbed dynamical system. The detection of chaotic trajectory in the perturbed system is accomplished through the utilization of a variety of tools designed for chaos detection. The execution of the Runge–Kutta method is employed to assess the sensitivity of the examined model. The results obtained serve to underscore the effectiveness and applicability of the proposed methodologies for the assessment of soliton structures within a broad spectrum of nonlinear models.

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Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

Riaz,

Jhangeer,

Martinovic

et al. 2024

Nonlinear Engineering

View full text Add to dashboard Cite

show abstract

Analytical solutions to a class of fractional coupled nonlinear Schrödinger equations via Laplace-HPM technique

Hong

Wang

2023

MATH

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<abstract> <p>In this article, a class of fractional coupled nonlinear Schrödinger equations (FCNLS) is suggested to describe the traveling waves in a fractal medium arising in ocean engineering, plasma physics and nonlinear optics. First, the modified Kudryashov method is adopted to solve exactly for solitary wave solutions. Second, an efficient and promising method is proposed for the FCNLS by coupling the Laplace transform and the Adomian polynomials with the homotopy perturbation method, and the convergence is proved. Finally, the Laplace-HPM technique is proved to be effective and reliable. Some 3D plots, 2D plots and contour plots of these exact and approximate solutions are simulated to uncover the critically important mechanism of the fractal solitary traveling waves, which shows that the efficient methods are much powerful for seeking explicit solutions of the nonlinear partial differential models arising in mathematical physics.</p> </abstract>

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Solution of Sakata-Taketani Equation via the Caputo and Riemann-Liouville Fractional Derivatives

Cited by 2 publications

References 17 publications

Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

Analytical solutions to a class of fractional coupled nonlinear Schrödinger equations via Laplace-HPM technique

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