Instability modulation and novel optical soliton solutions to the Gerdjikov–Ivanov equation with M-fractional

Ismael, Hajar F.; Başkonuş, Hacı Mehmet; Gao, Wei

doi:10.1007/s11082-023-04581-7

Cited by 24 publications

(10 citation statements)

References 43 publications

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“…Definition. Let p(t) be a function identified for all non-negative t. Then, the beta derivative of p(t) is given by [26][27][28]…”

Section: Preliminariesmentioning

confidence: 99%

New soliton solutions of kraenkel-manna-merle system with beta time derivative

Bayrakci,

Tuluce Demiray,

Yildirim

2023

Phys. Scr.

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This article discusses the fractional Kraenkel-Manna-Merle (KMM) system, which describes the motion of a nonlinear ultrashort wave pulse through saturated ferromagnetic materials with zero conductivity. The fractional behavior of this system was investigated using the beta derivative. The modified generalized exponential rational function method (MGERFM), developed by modifying the generalized exponential rational function method (GERFM), is applied to this system for the first time. Thus, some soliton solutions of the KMM system that have not been obtained before are presented for the first time in this study. In addition, 2D, 3D and density graphs of the obtained solutions for various values and ranges are presented. Discussions of these graphs are given and the found solutions are compared with other solutions.

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“…Definition. Let p(t) be a function identified for all non-negative t. Then, the beta derivative of p(t) is given by [26][27][28]…”

Section: Preliminariesmentioning

confidence: 99%

New soliton solutions of kraenkel-manna-merle system with beta time derivative

Bayrakci,

Tuluce Demiray,

Yildirim

2023

Phys. Scr.

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“…Its significance in research drives the exploration of diverse forms of OSs. Multiple methodologies have been established to generate OS solutions for such models, including the modified (G′/G)-expansion method 8 – 10 , the unified method 11 , 12 , the modified double Laplace transform scheme 13 , the adapted exponential task scheme 14 , the symbolic computational approach 15 , generalized Riccati equation mapping 16 , mapping method 17 , the φ6-model expansion approach 18 , sine–Gordon expansion method 19 , the improved Kudryashov’s approach 20 , Lie symmetry analysis 21 , the New generalized auxiliary equation method 22 , binary Darboux transformations 23 , among many others.…”

Section: Introductionmentioning

confidence: 99%

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Refaie Ali,

Alam,

Parven

2024

Sci Rep

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The space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons.

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“…In calculus, the chain rule, which holds great importance, is discussed regarding fractional derivatives in [8]. Moreover, fractional derivatives find frequent use in numerical analysis, as evidenced by studies [9,10]. The applications of fractional calculus extend to various scientific and engineering domains.…”

Section: Introductionmentioning

confidence: 99%

Fractional Curvatures of Equiaffine Curves in Three-Dimensional Affine Space

Öğrenmiş

2024

Journal of New Theory

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This paper presents a method for computing the curvatures of equiaffine curves in three-dimensional affine space by utilizing local fractional derivatives. First, the concepts of $\alpha$-equiaffine arc length and $\alpha$-equiaffine curvatures are introduced by considering a general local involving conformable derivative, V-derivative, etc. In fractional calculus, equiaffine Frenet formulas and curvatures are reestablished. Then, it presents the relationships between the equiaffine curvatures and $\alpha$-equiaffine curvatures. Furthermore, graphical representations of equiaffine and $\alpha$-equiaffine curvatures illustrate their behavior under various conditions.

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Instability modulation and novel optical soliton solutions to the Gerdjikov–Ivanov equation with M-fractional

Cited by 24 publications

References 43 publications

New soliton solutions of kraenkel-manna-merle system with beta time derivative

New soliton solutions of kraenkel-manna-merle system with beta time derivative

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Fractional Curvatures of Equiaffine Curves in Three-Dimensional Affine Space

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