Browsing by Author "Bayram, Mustafa"

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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 S.A., 2019) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Bayram, Mustafa; 56389
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).
Families of exact solutions of Biswas-Milovic equation by an exponential rational function method
(2020) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Bayram, Mustafa; 56389
In this paper, we introduce generalized exponential rational function method (GERFM) to obtain an exact solutions for the Biswas-Milovic (BM) equation with quadratic-cubic and parabolic nonlinearities. A wide range of closed solutions are acquired. The most important feature of the new method is that it is very effective and simple. The main merits of the proposed is that it gives more general solutions with some free parameters and can be applied to other types of nonlinear partial differential equations.Some interesting Figures for the physical features of some of the obtained solutions are also presented.
On Numerical Solution of the Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu-Caputo Derivative
(2020) Baleanu, Dumitru; Inc, Mustafa; Bayram, Mustafa; Baleanu, Dumitru; 56389
A powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): ABCDβ 0+, t u(x,t) = ζuxx(x,t) - κux(x,t) + F(x, t), 0 < β ≤ 1. The time-fractional derivative ABCDβ 0 + ,t u(x,t) is described in the Atangana-Baleanu Caputo concept. The basis of our approach is transforming the original equation into a new equation by imposing a transformation involving a fictitious coordinate. Then, a geometric scheme namely the group preserving scheme (GPS) is implemented to solve the new equation by taking an initial guess. Moreover, in order to present the power of the presented approach some examples are solved, successfully. © 2019 M. Partohaghighi et al.
Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes
(2019) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; 56389
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.
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) Baleanu, Dumitru; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; 56389
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.
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) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; 56389
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.
Theory and application for the time fractional Gardner equation with Mittag-Leffler kernel
(Taylor&Francis LTD, 2019) Baleanu, Dumitru; İnç, Mustafa; Baleanu, Dumitru; Bayram, Mustafa; 56389
In this work, the time fractional Gardner equation is presented as a new fractional model for Atangana-Baleanu fractional derivative with Mittag-Leffler kernel. The approximate consequences are analysed by applying a recurrent process. The existence and uniqueness of solution for this system is discussed. To explain the effects of several parameters and variables on the movement, the approximate results are shown in graphics and tables.
Two-wave, breather wave solutions and stability analysis to the (2+1)-dimensional Ito equation
(2022) Baleanu, Dumitru; Yusuf, Abdullahi; Hincal, Evren; Baleanu, Dumitru; Bayram, Mustafa; 56389
The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed phys-ical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study's findings may help explain the physics behind some of the chal-lenges facing ocean engineers.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )