Person: AKBULUT, ARZU
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AKBULUT
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ARZU
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Publication Some latest families of exact solutions to date-jimbo-kashiwara-miwa equation and its stability analysis(Mdpi, 2023-10-01) Alqahtani, Rubayyi T.; Alharthi, Nadiyah Hussain; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/ Matematik Bölümü.; 0000-0003-2448-2481; F-5393-2015The present study demonstrates the derivation of new analytical solutions for the Date-Jimbo-Kashiwara-Miwa equation utilizing two distinct methodologies, specifically the modified Kudryashov technique and the (g')-expansion procedure. These innovative concepts employ symbolic computations to provide a dynamic and robust mathematical procedure for addressing a range of nonlinear wave situations. Additionally, a comprehensive stability analysis is performed, and the acquired results are visually represented through graphical representations. A comparison between the discovered solutions and those already found in the literature has also been performed. It is anticipated that the solutions will contribute to the existing literature related to mathematical physics and soliton theory.Publication Obtaining the soliton type solutions of the conformable time-fractional complex ginzburg-landau equation with kerr law nonlinearity by using two kinds of kudryashov methods(Hindawi, 2023-02-04) Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-2448-2481; F-5393-2015The main idea of this study is to obtain the soliton-type solutions of the conformable time-fractional complex Ginzburg-Landau equation with Kerr law nonlinearity. For this aim, the generalized and modified Kudryashov methods are applied to the given model. The reason for using a conformable derivative is that the chain rule can be applied to this derivative. Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. According to our results, both of the used methods are effective and powerful. Finally, 3D and contour plots are given for some results with suitable variables. Our findings in this paper are critical for explaining a wide range of scientific and physical applications. According to our knowledge, our results are new in the literature.Publication Some exact solitons to the (2+1)-dimensional broer-kaup-kupershmidt system with two different methods(Springer, 2023-12-01) Malik, Sandeep; Kumar, Sachin; Rezazadeh, Hadi; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; F-5393-2015The exact solutions of the (2 + 1) dimensional Broer-Kaup-Kupershmidt (BKK) system which has been recommended to model the nonlinear and dispersive long gravity waves traveling along with the two horizontal directions in the shallow water of uniform depth were obtained. Firstly, the given system was reduced to an ordinary differential equation (ODE) with the help of the wave transformations. Then, the reduced ODE was solved with the help of two methods which are called the modified (G'/G)-expansion method and new extended generalized Kudryashov method. We checked the results with the Maple software and plotted 3D, contour and 2D plots of some obtained solutions. As a result, we obtained exact solutions that are different from each other and have not been obtained before. Results can enhance the nonlinear dynamical behavior of a given system and demonstrate the effectiveness of the employed methodology. Results will be beneficial to a large number of engineering model specialists and useful for understanding the wave motions.Publication Triki-biswas model: Its symmetry reduction, nucci's reduction and conservation laws(World Scientific Publ Co Pte, 2022-10-05) Akbulut, Arzu; Mirzazadeh, M.; Hashemi, M. S.; Hosseini, K.; Salahshour, S.; Park, C.; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; F-5393-2015In this paper, the symmetry reduction method and Nucci's reduction method are used to obtain exact solutions to the Triki-Biswas equation. Furthermore, the new conservation theorem is utilized for finding the conservation laws of the given model. The conservation laws are derived for each admitted symmetry of the Triki-Biswas equation and satisfy the divergence condition. The 3D, contour and 2D figures are finally plotted to show the dynamics of the obtained exact solutions.Publication A novel scheme for SMCH equation with two different approaches(Univ Tabriz, 2023-01-01) Akbulut, Arzu; İslam, S. M. Rayhanul; Arafat, S. M. Yasir; Taşcan, Filiz; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-2448-2481; F-5393-2015In this study, the unified and improved F-expansion methods are applied to derive exact traveling wave solutions of the simplified modified Camassa-Holm (SMCH) equation. The current methods can calculate all branches of solutions at the same time, even if several solutions are quite near and therefore impossible to identify via numerical methods. All obtained solutions are given by hyperbolic, trigonometric, and rational function solutions which obtained solutions are useful for real-life problems in fluid dynamics, optical fibers, plasma physics and so on. The two-dimensional (2D) and three-dimensional (3D) graphs of the obtained solutions are plotted. Finally, we can state that these strategies are extremely successful, dependable, and simple. These ideas might potentially be applied to many nonlinear evolution models in mathematics and physics.Publication Optical solitons of the perturbation fokas-lenells equation by two different integration procedures(Elsevier Gmbh, 2022-12-17) Elsherbeny, Ahmed M.; Mirzazadeh, Mohammad; Arnous, Ahmed H.; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-3635-7090; 0000-0003-2448-2481; F-5393-2015In this study, the general projective Riccati equations and the enhanced Kudryashov's methods are presented for the optical solitons of the perturbation Fokas-Lenells (FL) equation. For this aim, the perturbation Fokas-Lenells equation is converted to a nonlinear ordinary differential equation via wave transformations. Then, the balance number is calculated by the homogeneous balance method. Then, the used methods are applied to the given model. Finally, three-dimensional, contour, and two-dimensional figures of the results are presented. According to the obtained results, both methods are effective and powerful. The obtained results are significant in mathematical physics, soliton theory, and many other areas.Publication On the dynamics of the complex hirota-dynamical model(Mdpi, 2023-12-01) Kaplan, Melike; Alqahtani, Rubayyi T.; Ahmed, W. Eltayeb; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0003-2448-2481; F-5393-2015The complex Hirota-dynamical Model (HDM) finds multifarious applications in fields such as plasma physics, fusion energy exploration, astrophysical investigations, and space studies. This study utilizes several soliton-type solutions to HDM via the modified simple equation and generalized and modified Kudryashov approaches. Modulation instability (MI) analysis is investigated. We also offer visual representations for the HDM.Publication Solitary wave solutions of coupled nerve fibers model based on two analytical techniques(Springer, 2023-07-01) Razzaq, Waseem; Zafar, Asim; Kaplan, Melike; Raheel, M.; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; F-5393-2015This paper focuses on a few innovative solutions to the coupled nerve fibers model. The constructed solutions can be used to expose this model in a noticeable way. The verified solutions are including the trigonometric, exponential, and hyperbolic functions. Utilizing the Mathematica tool, the results are verified. We employed two approaches, named as modified extended tanh expansion and modified (G' G(2) )-expansion methods, to obtain the results. We gave the 2-D and 3-D plots of the obtained results. The obtained results are dissimilar from previous results in the literature. The used methods are powerful and effective. The obtained results have potential to be conducive for the model's future development.