Yazar "Isah, Muhammad Abubakar" seçeneğine göre listele

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    Dynamical behaviors of different wave structures to the Korteweg–de Vries equation with the Hirota bilinear technique
    (Elsevier, 2023) Yokus, Asıf; Isah, Muhammad Abubakar
    This work uses the new exponential rational function and a Hirota bilinear technique to solve the Korteweg–de Vries equation. This method generates several exact solutions, most of which are new in various forms of solitons. Some of the obtained soliton solutions are used to find the breather solutions of the equation via an exponential function. The linear stability technique is used to study the stability of the derived solutions using the stability analysis. All of the obtained solutions are stable and exact solutions that have also been put into the equation to ensure their existence which are graphically shown as well. It makes constructive contributions to science by formulating nonlinear wave distribution and the dynamic behavior of wave systems, which are a part of real life. From both a mathematical and physical standpoint, the derived wave function via the new homoclinic approach has been examined and discussed. This research also involves an in-depth examination of nonlinear longwave propagation using the newly discovered soliton. The effects of forces acting on a solitary wave, which has elastic dispersion, on nonlinear advection, dispersion and collision mechanisms are discussed. In this study, which allows making predictions about the environment in which the wave propagates, the physical interpretations of the dynamics affecting the solitaire are supported by graphics. The acquired findings indicate the generality and effectiveness of the used approach.
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    Exploring the influence of layer and neuron configurations on Boussinesq equation solutions via a bilinear neural network framework
    (Springer Science and Business Media B.V., 2024) Isah, Muhammad Abubakar; Yokus, Asif; Kaya, Doğan
    This study examines the Boussinesq equation, which is a nonlinear partial differential equation used to describe long wave propagation in shallow water and has broader applications, including nonlinear lattice waves, vibrations in nonlinear strings, and ion sound waves in plasma. The Boussinesq equation provides an insight into the nonlinear long wave propagation behavior in shallow water by taking wave phase into account. Its versatility extends its utility beyond fluid dynamics to various physical phenomena. By providing specific activation functions in the ``2-3-1?? and ``2-5-1?? neural network models, respectively, the generalized lump solution and the precise analytical solutions are produced using the bilinear neural network approach. These analytical solutions, together with the related rogue waves, dark soliton, and bright soliton, are derived using symbolic computation. These findings fill in the gaps in the current research about the Boussinesq equation. The dynamical properties of these waves are displayed on three-dimensional, contour, density, and two-dimensional graphs. The response of the wave solution to different values of wave speed in relation to the wave phase it contains has been described with the help of wave intensity. In addition, the advantages and disadvantages of the layers used in the analytical technique to generate solutions have been discussed. The efficient techniques employed in this research are useful for studying the nonlinear differential equations in one-dimensional nonlinear lattice waves, vibrations in a nonlinear string, and ion sound waves in plasma.
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    Nonlinear Dispersion Dynamics of Optical Solitons of Zoomeron Equation with New φ6Model Expansion Approach
    (L and H Scientific Publishing, LLC, 2024) Isah, Muhammad Abubakar; Yokus, Asif
    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 method of ?6-model expansion 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 velocities do 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. The nonlinear dispersion behavior is analyzed for different values of the magnitude, which physically represents the wave velocity, from the parameters of the generated traveling wave solutions. Interesting graphs are employed to explain and highlight the dynamical aspects of the results, and all of the obtained results are put into the Zoomeron equation to show the accuracy of the results.
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    The novel optical solitons with complex Ginzburg–Landau equation for parabolic nonlinear form using the ϕ6-model expansion approach
    (Cambridge Scientific Publishers, 2023) Yokuş, Asıf; Isah, Muhammad Abubakar
    This work investigates the complex Ginzburg–Landau equation (CGLE) with parabolic law in nonlinear optics, this form of nonlinearity may also be seen in fiber optics. It is referred to as the fifth-order susceptibility, which is predominantly present in a transparent glass with intense femtosecond pulses at 620nmI. The ?6-model expansion approach is used to find dark, singular, periodic, and combined optical soliton solutions to the model. The results presented in this study are intended to improve the CGLE’s nonlinear dynamical characteristics. These solitons are significant resources in physics and telecommunications engineering. They led to several quick follow-up investigations. 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. Some of the obtained solutions’ 2-, 3-dimensional, and contour plots are shown.
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    A novel technique to construct exact solutions for the Complex Ginzburg-Landau equation using quadratic-cubic nonlinearity law
    (Cambridge Scientific Publishers, 2023) Isah, Muhammad Abubakar; Yokuş, Asıf
    The Complex Ginzburg-Landau equation (CGLE) has been suggested and investigated as a model for turbulent dynamics in nonlinear partial differential equations. It is a particularly intriguing model in this aspect since it is a dissipative form of the nonlinear Schrödinger equation. The model is studied with quadratic-cubic law nonlinear fiber by using ?6–model expansion method, bright, dark, dark-singular, singular and dark-bright optical soliton solutions are obtained. The findings of this study might 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 cosine function is the shape of a hanging cable (the so-called catenary). Finally, there are some discussions regarding new complex solutions, it is explored by giving physical meaning to the constants found in traveling wave solutions, which are both physically and mathematically significant. The three-dimensional, two-dimensional simulations and contour plots are used to enhance these discussions.
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    Optical solitons of the complex Ginzburg–Landau equation having dual power nonlinear form using φ6-model expansion approach
    (Mehmet Yavuz, 2023) Isah, Muhammad Abubakar; Yokus, Asif
    This paper employs a novel ? 6 -model expansion approach to get dark, bright, periodic, dark-bright, and singular soliton solutions to the complex Ginzburg-Landau equation with dual power-law non linearity. The dual-power law found in photovoltaic materials is used to explain nonlinearity in the refractive index. The results of this paper may assist in comprehending some of the physical effects of various nonlinear physics models. For example, the hyperbolic sine arises in the calculation of the Roche limit and the gravitational potential of a cylinder, the hyperbolic tangent arises in the calculation of the magnetic moment and the rapidity of special relativity, and the hyperbolic cotangent arises in the Langevin function for magnetic polarization. Frequency values, one of the soliton’s internal dynamics, are used to examine the behavior of the traveling wave. Finally, some of the obtained solitons’ three-, two-dimensional, and contour graphs are plotted.
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    Rogue waves and Stability Analysis of the new (2+1)-KdV Equation Based on Symbolic Computation Method via Hirota Bilinear Form
    (Institute of Electrical and Electronics Engineers Inc., 2023) Isah, Muhammad Abubakar; Yokus, Asif
    In this article, we study the novel KdV model which makes a significant contribution to the understanding of a variety of nonlinear occurrences of ion-acoustic waves in plasma and acoustic waves in harmonic crystals. Hirota bilinearization will be used to carry out the task via the proper transformations. For various polynomial functions, several soliton solution types, specifically kink and rogue wave solutions, will be examined. We also present a kink wave and rogue wave interaction solution. The discovered solutions will be illustrated graphically. The existing work is widely used to report a variety of fascinating physical occurrences in the domains of shallow-water waves, ion-acoustic waves in plasma and acoustic waves in harmonic crystals.
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    Stability Analysis and Soliton Solutions of the Nonlinear Evolution Equation by Homoclinic Technique Based on Hirota Bilinear Form
    (Institute of Electrical and Electronics Engineers Inc., 2023) Yokus, Asif; Isah, Muhammad Abubakar
    The novel KdV model plays a significant part in the discovery of a variety of nonlinear ion acoustic wave and harmonic crystal phenomena. The new homoclinic method based on the Hirota bilinear form is used to create the bilinear form of the new KdV equation and uncover numerous new exact solu tions. The stability of the solutions is studied in this article using the modulation instability. The results show novel mechanical structures and new properties for this evolution equation. The physical dynamics of the traveling wave solutions produced by the recently suggested homoclinic approach to reinforce the Hirota bilinear method are investigated, the obtained solutions are represented using 2?dimensional, 3?dimensional and contour plots. To guarantee their existence, all the solutions that have been found are inserted into the model. These results open up a new opportunity for us to thoroughly investigate the model. Numerous exciting physical occurrences in the fields of shallow-water waves, ion-acoustic waves in plasma, acoustic waves in harmonic crystal and other related phenomena are reported using the existing work on a regular basis