Yazar "Yusuf, Abdullahi" seçeneğine göre listele

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    Dark-Bright Optical Soliton and Conserved Vectors to the Biswas-Arshed Equation With Third-Order Dispersions in the Absence of Self-Phase Modulation
    (FRONTIERS MEDIA SA, AVENUE DU TRIBUNAL FEDERAL 34, LAUSANNE, CH-1015, SWITZERLAND, 2019) Aliyu, Aliyu Ise; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Bayram, Mustafa
    The form-I version of the new celebrated Biswas-Arshed equation is studied in this work with the aid of complex envelope ansatz method. The equation is considered when self-phase is absent and velocity dispersion is negligibly small. New Dark-bright optical soliton solution of the equation emerge from the integration. The acquired solution combines the features of dark and bright solitons in one expression. The solution obtained are not yet reported in the literature. Moreover, we showed that the equation possess conservation laws (Cls).
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    Invariant Investigation and Exact Solutions of Some Differential Equations with Conformable Derivatives
    (Amer Scientific Publishers, 2018) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Bayram, Mustafa
    In this work, the conformable Harry-Dym, conformable logarithmic-KdV and conformable Zakharov-Ito equations are studied by using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the partial differential equations (PDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, polynomial and trigonometric function solutions are derived. Ultimately, for illustrating the acquired results, some numerical simulations are performed.
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    On the soliton solutions to the density-dependent space time fractional reaction-diffusion equation with conformable and M-truncated derivatives
    (Springer, 2023) Esen, Handenur; Ozdemir, Neslihan; Secer, Aydin; Bayram, Mustafa; Sulaiman, Tukur Abdulkadir; Ahmad, Hijaz; Yusuf, Abdullahi
    In this manuscript, the density-dependent space-time fractional reaction-diffusion equation in the sense of conformable and M-truncated derivatives (CMD) is presented. Through fractional transformation, these nonlinear fractional equations can be converted into nonlinear ordinary differential equations (NLPDEs). Besides, with the help of the Riccati-Bernoulli sub-ODE method (RBM), new exact solutions for these nonlinear fractional equations are produced. In order to construct the comparative analysis between different type fractional derivatives, graphical representations are demonstrated for chosen values of unknown parameters.
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    Optical solitons and other solutions to the Hirota-Maccari system with conformable, M-truncated and beta derivatives
    (World Scientific Publ Co Pte Ltd, 2022) Ozdemir, Neslihan; Esen, Handenur; Secer, Aydin; Bayram, Mustafa; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir
    In this research paper, we scrutinize the novel traveling wave solutions and other solutions with conformable, M-truncated and beta fractional derivatives for the nonlinear fractional Hirota-Maccari system. In order to acquire the analytical solutions, the Riccati-Bernoulli sub-ODE technique is implemented. Presented method is the very powerful technique to get the novel exact soliton and other solutions for nonlinear partial equations in sense of both integer and fractional-order derivatives. Mathematical properties of different kinds of fractional derivatives are given in this paper. A comparative approach is presented between the solutions with the fractional derivatives. For the validity of the solutions, the constraints conditions are determined. To illustrate the physical meaning of the presented equation, the 2D and 3D graphs of the acquired solutions are successfully charted by selecting appropriate values of parameters.
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    Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes
    (World Scientific Publ Co Pte Ltd, 2019) Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru
    In this study, two integration techniques are employed to reach optical solitons to the (n + 1)-dimensional nonlinear Schrodinger's equation ((n + 1)-NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.
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    Solitary wave solutions of chiral nonlinear Schrodinger equations
    (World Scientific Publ Co Pte Ltd, 2021) Esen, Handenur; Ozdemir, Neslihan; Secer, Aydin; Bayram, Mustafa; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi
    This paper presents the (1+1)-dimensional chiral nonlinear Schrodinger equation (1DCNLSE) and (2+1)-dimensional chiral nonlinear Schrodinger equation (2DCNLSE) that define the edge states of the fractional quantum hall effect. In this paper, we implement the Riccati-Bernoulli sub-ODE method in reporting the solutions of these two nonlinear physical models. As a result of this, some singular periodic waves, dark and singular optical soliton solutions are generated for these models. Some of the acquired solutions are illustrated by three-dimensional (3D) and two-dimensional (2D) graphs utilizing suitable values of the parameters with the help of the MAPLE software to demonstrate the importance in the real-world of the presented equations.
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    Soliton Solutions for Kudryashov-Sinelshchikov Equation
    (YILDIZ TECHNICAL UNIV, YILDIZ CAMPUS, BESIKTAS, ISTANBUL, 34349, TURKEY, 2019) Yusuf, Abdullahi; İnç, Mustafa; Bayram, Mustafa
    This paper acquires the closed form solutions for the Kudryashov-Sinelshchikov (KS) equation. The Riccati-Bernoulli (RB) sub-ODE method is used to acquire such solitons whose structure include trigonmetric, hyperbolic and algebraic structures. Some interesting figures for the obtained solutions are presented in order to shed light on the characteristics of the solutions.
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    SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION
    (Yildiz Technical Univ, 2019) Yusuf, Abdullahi; Inc, Mustafa; Bayram, Mustafa
    This paper acquires the closed form solutions for the Kudryashov-Sinelshchikov (KS) equation. The Riccati-Bernoulli (RB) sub-ODE method is used to acquire such solitons whose structure include trigonmetric, hyperbolic and algebraic structures. Some interesting figures for the obtained solutions are presented in order to shed light on the characteristics of the solutions.
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    Stability Analysis and Conservation Laws via Multiplier Approach for the Perturbed Kaup-Newell Equation
    (Amer Scientific Publishers, 2018) Yusuf, Abdullahi; Inc, Mustafa; Bayram, Mustafa
    This paper presents the stability analysis (SA) and the conservation laws (Cls) for the perturbed Kaup-Newell equation (pKNE) by using the stability analysis technique and the multiplier method, respectively. The pKNE was recently introduced from a generalized Kaup-Newell spectral problem with linear perturbation with an arbitrary constant beta. In a situation where by beta = 0 one reaches the standard Kaup-Newell equation which possesses a tri-Hamiltonian feature and is the Euler-Poincare flow on the space of first order differential operator.
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    Symmetry reductions, explicit solutions, convergence analysis and conservation laws via multipliers approach to the Chen-Lee-Liu model in nonlinear optics
    (World Scientific Publ Co Pte Ltd, 2019) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru
    In this paper, symmetry analysis is performed for the nonlinear Chen-Lee-Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach.