Yazar "Faridi, Waqas Ali" seçeneğine göre listele

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    Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm
    (Elsevier B.V., 2021) Jhangeer, Adil; Faridi, Waqas Ali; Asjad, Muhammad Imran; Akgül, Ali
    This paper aims to study an improved perturbed Schrödinger equation (IPSE) with a kind of Kerr law non-linearity equation governing the propagation dynamics of soliton in optical fibers through the nano-optical fiber. The considered model predicts the influence of quantic non-linearity on the motion of ultrashort optical pulses. The integrability of the model is accompanied by the transformed rational function V-expansion method (for simplicity [Formula presented]). This proposed method is a significant mathematical tool to obtain the exact travelings wave solutions of non-linear complex partial differential equations (PDEs). A bunch of soliton solutions like dark, dark singular, plane wave solution, and periodic are retrieved along with suitable parametric values. The graphical analysis is also presented for the description of propagation of waves expressed by rational functions, hyperbolic functions, and trigonometric functions. © 2021 The Author(s)
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    Exact fractional soliton solutions of thin-film ferroelectric material equation by analytical approaches
    (Elsevier, 2023) Faridi, Waqas Ali; Abu Bakar, Muhammad; Akgul, Ali; Abd El-Rahman, Magda; Din, Sayed M. El
    In this paper, the main motive is to mathematical explore the thin-film ferroelectric material partial differential equation which addresses the Ferroelectrics, that are being examined as key materials for applications in piezoelectric, pyroelectric electrostrictive, linear, and nonlinear optical systems. Thin ferroelectric films are used in a variety of modern electrical devices because they are both nonlinear ferroelectric and dielectric materials. This article appropriates the fractional travelling wave transformation allowing the partial differential equation to be changed into an ordinary differential equation. The considered fractional model is explored through employing the combo of ??????& PRIME; ??????2-expansion method and new extended direct algebraic methodology. As an outcome, numerous types of soliton solutions like, Periodic pattern with anti-peaked crests and anti-troughs, singular solution, mixed complex solitary shock solution, mixed singular solution, mixed shock singular solution, mixed trigonometric solution, mixed periodic, periodic solution and mixed hyperbolic solution obtain via Mathematica. In addition, the ??????& PRIME; ??????2-expansion technique produces singular, trigonometric, and hyperbolic solutions with different soliton families. The revealed solution will improve the mathematical analysis of this model and the associated physical phenomenon's. In order to visualize the graphical propagation of the obtained fractional soliton solutions, 3D, 2D, and contour graphics are generated by choosing appropriate parametric values. The impact of fractional parameter ?????? is also graphically displayed on the propagation of solitons.
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    Novel solitonic structure, Hamiltonian dynamics and lie symmetry algebra of biofilm
    (Elsevier B.V., 2024) Asghar, Umair; Asjad, Muhammad Imran; Faridi, Waqas Ali; Akgül, Ali
    In this study, the Lie point symmetries and optimal system have been established. We discuss the biofilm model's soliton solutions. To examine a nonlinear dynamical biofilm system, which is simply a bistable Allen–Cahn equation with quartic potential, to determine solitary wave profiles using the considered equation, a new auxiliary equation technique is used. A suitable variable transformation is used to convert the governing equation into a nonlinear ordinary differential equation. The unified approach is utilized to evaluate periodic solutions, solitary and soliton solutions as well as several newly discovered exact solitary wave solutions, it can be accomplished via Mathematica (https://www.wolfram.com/mathematica/online/). The new auxiliary equation approach is an efficient method for creating unique wave profiles based on a variety of soliton families. Also, the results are graphically visualized, by using the appropriate parametric settings. The outcomes are shown graphically in two dimensions, three dimensions, and contour form. The Hamiltonian conditions are satisfied by the planer dynamical framework of equations to ensure as the system that was generated is a conservative Hamiltonian dynamical system which includes all traveling wave structures. A sensitivity evaluation is used to explore the governing model's thoroughly dynamical properties. It is demonstrated that the model becomes more dependent on the beginning conditions than the variables. The strategy could be used to look for exact solutions to various nonlinear evolution equations. We believe that this study will have important applications in different areas of science. © 2024 The Author(s)
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    The computation of Lie point symmetry generators, modulational instability, classification of conserved quantities, and explicit power series solutions of the coupled system
    (Elsevier, 2023) Faridi, Waqas Ali; Yusuf, Abdullahi; Akgul, Ali; Tawfiq, Ferdous M. O.; Tchier, Fairouz; Al-deiakeh, Rawya; Sulaiman, Tukur A.
    The well-known Chaffee-Infante reaction hierarchy is examined in this article along with its reaction-diffusion coupling. It has numerous variety of applications in modern sciences, such as electromagnetic wave fields, fluid dynamics, high-energy physics, ion-acoustic waves in plasma physics, coastal engineering, and optical fibres. The physical processes of mass transfer and particle diffusion might be expressed in this way. The Lie invariance criteria is taken into consideration while we determine the symmetry generators. The suggested approach produces the six dimensional Lie algebra, where translation symmetries in space and time are associated to mass conservation and conservation of energy respectively, the other symmetries are scaling or dilation. Additionally, similarity reductions are performed, and the optimal system of the sub-algebra should be quantified. There are an enormous number of exact solutions can construct for the traveling waves when the governing system is transformed into ordinary differential equations using the similarity transformation technique. The power series approach is also utilized for ordinary differential equations to obtain closed -form analytical solutions for the proposed diffusive coupled system. The stability of the model under the limitations is ensured by the modulation instability analysis. The reaction diffusion hierarchy's conserved vectors are calculated using multiplier methods using Lie Backlund symmetries. The acquired results are presented graphically in 2-D and 3-D to demonstrate the wave propagation behavior.
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    The construction of exact solution and explicit propagating optical soliton waves of Kuralay equation by the new extended direct algebraic and Nucci's reduction techniques
    (Taylor & Francis Inc, 2024) Faridi, Waqas Ali; Myrzakulova, Zhaidary; Myrzakulov, Ratbay; Akguel, Ali; Osman, M. S.
    The aim of this paper is to investigate the integrable motion of induced curves using the Kuralay equation, which is a complex integrable coupled system. The soliton solutions derived from Kuralay equation are supposed to represent the most advanced research in several significant phenomena, including optical fibers, nonlinear optics, and ferromagnetic materials. Analytical methods are used to obtain traveling wave solutions for this model as the Cauchy problem cannot be addressed by the inverse scattering transform. In order to find the solitary wave solutions, the new extended direct algebraic and Nucci's reduction approaches are taken over. As a result, the new extended direct algebraic method provides singular, mixed singular, periodic, mixed trigonometric, complex combo, trigonometric, mixed hyperbolic, plane, and combined bright-dark soliton solutions. The Nucci's reduction technique develops the first integral of differential equation to discuss the conservation and exact solutions. To ensure the sensitivity of the study, the effect of waves on the propagation of solitons and the sensitivity of the model is examined. To illustrate how the fitting values of the system parameters may be utilized to anticipate the behavioral reactions to pulse propagation, the resulting solutions are visually shown in 2D and 3D charts.
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    The formation of solitary wave solutions and their propagation for Kuralay equation
    (Elsevier, 2023) Faridi, Waqas Ali; Abu Bakar, Muhammad; Myrzakulova, Zhaidary; Myrzakulov, Ratbay; Akgul, Ali; El Din, Sayed M.
    In this paper, the main motive is to mathematical explore the Kuralay equation, which find applications in various fields such as ferromagnetic materials, nonlinear optics, and optical fibers. The objective of this study is to investigate different types of soliton solutions and analyze the integrable motion of induced space curves. This article appropriates the traveling wave transformation allowing the partial differential equation to be changed into an ordinary differential equation. To establish these soliton solutions, the study employs the new auxiliary equation method. As an outcome, a numerous types of soliton solutions like, Periodic pattern with anti-peaked crests and anti-troughs, singular solution, mixed complex solitary shock solution, mixed singular solution, mixed shock singular solution, mixed trigonometric solution, mixed periodic, periodic solution and mixed hyperbolic solution obtain via Mathematica. In order to visualize the graphical propagation of the obtained soliton solutions, 3D, 2D, and contour graphics are generated by choosing appropriate parametric values. The impact of parameter w is also graphically displayed on the propagation of solitons.
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    The Propagating Exact Solitary Waves Formation of Generalized Calogero-Bogoyavlenskii-Schiff Equation with Robust Computational Approaches
    (Mdpi, 2023) Al Alwan, Basem; Abu Bakar, Muhammad; Faridi, Waqas Ali; Turcu, Antoniu-Claudiu; Akgul, Ali; Sallah, Mohammed
    The generalized Calogero-Bogoyavlenskii-Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero-Bogoyavlenskii-Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures.