Person: AKBULUT, ARZU
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AKBULUT
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ARZU
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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 Investigation of solitons and conservation laws in an inhomogeneous optical fiber through a generalized derivative nonlinear schrodinger equation with quintic nonlinearity(Springer, 2023-09-01) Rabie, Wafaa B. B.; Ahmed, Hamdy M. M.; Mirzazadeh, Mohammad; Hashemi, Mir Sajjad; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0003-2448-2481; F-5393-2015The current research investigates the behavior of femtosecond solitary waves in an inhomogeneous optical fiber using the generalized derivative nonlinear Schrodinger equation with quintic nonlinearity. The extended F-expansion technique is utilized to obtain various exact solutions such as bright soliton solutions, dark soliton solutions, combo bright-dark soliton solutions, singular soliton solutions, periodic solutions, Jacobi elliptic functions solutions, rational solutions, Weierstrass elliptic solutions, exponential solutions. The obtained solutions are presented in three-dimensional and contour graphics by selecting appropriate parameters. Ibragimov's conservation technique is also applied to obtain conservation laws for the given model. These findings are crucial for comprehending various of scientific and physical applications.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 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 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.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 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 New solitary wave patterns of the fokas system in fiber optics(Mdpi, 2023-04-01) Kaplan, Melike; Alqahtani, Rubayyi T.; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0003-2448-2481; F-5393-2015The Fokas system, which models wave dynamics using a single model of fiber optics, is the design under discussion in this study. Different types of solitary wave solutions are obtained by utilizing generalized Kudryashov (GKP) and modified Kudryashov procedures (MKP). These novel concepts make use of symbolic computations to come up with a dynamic and powerful mathematical approach for dealing with a variety of nonlinear wave situations. The results obtained in this paper are original and have the potential to be useful in mathematical physics.Publication Extraction of exact solutions of higher order sasa-satsuma equation in the sense of beta derivative(Mdpi, 2022-11-01) Fadhal, Emad; Kaplan, Melike; Awadalla, Muath; Abuasbeh, Kinda; Akbulut, Arzu; AKBULUT, ARZU; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0003-2448-2481; F-5393-2015Nearly every area of mathematics, natural, social, and engineering now includes research into finding exact answers to nonlinear fractional differential equations (NFDES). In order to discover the exact solutions to the higher order Sasa-Satsuma equation in the sense of the beta derivative, the paper will discuss the modified simple equation (MSE) and exponential rational function (ERF) approaches. In general, symmetry and travelling wave solutions of the Sasa-Satsuma equation have a common correlation with each other, thus we reduce equations from wave transformations to ordinary differential equations with the help of Lie symmetries. Actually, we can say that wave moves are symmetrical. The considered procedures are effective, accurate, simple, and straightforward to compute. In order to highlight the physical characteristics of the solutions, we also provide 2D and 3D plots of the results.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.