Special Curves According to Bishop Frame in Minkowski 3-Space

Isah, Muhammad Abubakar; Külahçı, Fatih

doi:10.2478/amns.2020.1.00021

Cited by 11 publications

(7 citation statements)

References 15 publications

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“…Euler's summation method only needs to take 12, 16 p q   to obtain the accuracy of 9 (10 ) O  and the average calculation time for each option is less than 2 milliseconds. To obtain the accuracy of 5 (10 ) O  , the Poisson summation method already requires 122880 p  calculations. The average time is 1184 milliseconds.…”

Section: Euler's Summation Methodsmentioning

confidence: 99%

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The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching

Yang

Zhang

Abdeldayem

2023

Applied Mathematics and Nonlinear Sciences

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It is more difficult to give Laplace transform directly in a defined form or derive it by Fourier transform in mathematics teaching. The article gives a solution for solving high exponential series sum by using Laplace transform. With the help of Laplace transform, calculus operations can be transformed into complex plane algebra operations. The application of the algorithm to the option hedging strategy verifies the applicability of the algorithm proposed in this article.

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Section: Euler's Summation Methodsmentioning

confidence: 99%

“…This gives the hedging error and the net value of the hedging account. It can be seen from Figure 3 that the benchmark hedges an underlying asset of 10 yuan without considering transaction friction [10]. This ultimately resulted in account equity.…”

Section: Numerical Simulation and Hedging Strategy Analysismentioning

confidence: 99%

The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching

Yang

Zhang

Abdeldayem

2023

Applied Mathematics and Nonlinear Sciences

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“…( 21), the periodic soliton solutions are obtained in Figure [2] and Figure [3] respectively. Figure [4] represents the 3D soliton solution graph of Eq. ( 27) for the parameters α 1 = −1.01, h 2 = 1.0001, c = 0.25, w = 0.007, y = 1, z = 1.…”

Section: If Lmentioning

confidence: 99%

“…The study of surfaces in geometry [1][2][3][4][5] and a wide range of issues in mechanics are where partial differential equations first appeared. Notable mathematicians from all over the world got actively interested in the study of a wide range of issues brought on by partial differential equations in the late 19th century.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons of Zoomeron equation by newly ϕ6-model expansion approach

Isah

Yokuş

2022

Preprint

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One of the equations describing incognito evolution, the nonlinear Zoomeron equation, is studied in this work. In a variety of physical circumstances, including laser physics, fluid dynamics and nonlinear optics, solitons with particular properties arise and the Zoomeron equation is a single example of one such situation. The Q^6-model expansion method allows for the explicit retrieval of a wide range of solution types, including kink-type solitons, these solitons are also called topological solitons in the context of water waves, their velocity does not depend on the wave amplitude, others are bright, singular, periodic and combined singular soliton solutions. The outcomes of this research may improve the Zoomeron equation's nonlinear dynamical features. The method proposes a practical and effective approach for solving a large class of nonlinear partial differential equations. Interesting graphs are employed to explain and highlight the dynamical aspects of the results, all of the obtained results are put into the Zoomeron equation to show the accuracy of the results.

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“…Partial differential equations were first employed for the study of surfaces in geometry [1,2,3,4,5] and a vast range of mechanical issues. Renowned mathematicians from throughout the world were keenly interested in studying a wide range of issues brought on by partial differential equations in the late 19th century [6].…”

Section: Introductionmentioning

confidence: 99%

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

Isah

Yokuş

2022

mmnsa

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This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The ϕ 6 -model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

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Special Curves According to Bishop Frame in Minkowski 3-Space

Cited by 11 publications

References 15 publications

The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching

The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching

Optical solitons of Zoomeron equation by newly ϕ6-model expansion approach

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

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