Person: SAĞLAM ÖZKAN, YEŞİM
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SAĞLAM ÖZKAN
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YEŞİM
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Publication A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws(Pergamon-Elsevier, 2021-02-01) Çelik, Nisa; Seadawy, Aly R.; Özkan, Yeşim Sağlam; Yaşar, Emrullah; ÇELİK, NİSA; SAĞLAM ÖZKAN, YEŞİM; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1364-5137; G-5333-2017; ITG-3498-2023; AAG-9947-2021In this study, we have dealt with a wave equation containing 4th order nonlinear mixed derivative. This model corresponds to solitary waves in nonlinear elastic circular rod. One dimensional optimal systems corresponding to Lie symmetry generator sub-algebras, symmetry reductions, and group invariant solutions corresponding to these systems have been systematically produced by Lie symmetry analysis of this model. In addition, traveling wave solutions were obtained with the help of an useful integration scheme of the model. These solutions are structures with physical properties of hyperbolic, trigonometric and rational solution types. Numerical simulations of the obtained solutions for different values of the parameters were made. The stability property of the obtained solutions is tested to show the ability of obtained solutions. In addition, the local conservation laws of the model were obtained with the help of the multiplier homotopy method.Publication Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications(Walter de Gruyter Gmbh, 2021-11-24) Özkan, Yeşim Sağlam; Yaşar, Emrullah; SAĞLAM ÖZKAN, YEŞİM; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1364-5137; 0000-0003-4732-5753; G-5333-2017; AAG-9947-2021The improved tan(phi/2)-expansion, simplest equation, and extended (G'/G)-expansion methods are employed to construct the exact solutions involving parameters of the Van der Waals equation arising in the material industry. This model explains the phase separation phenomenon. Understanding the prominent dynamic and static properties of this model and other models of this type is of great importance for the physical phenomena encountered in many areas of industry. Therefore, for such models, it is also important to obtain guiding solutions in obtaining new information. Many explicit wave solutions consisting of trigonometric, hyperbolic, rational, and exponential functions are found by using analytical techniques. The obtained solutions were verified with Maple by placing them back into the original equations. Moreover, graphical demonstrations for some of the obtained solutions are given.Publication Some properties of starlike functions subordinate to k-Pell-Lucas numbers(Springer, 2021-11-01) Altınkaya, Şahsene; Kara, Yeliz; Özkan, Yeşim Sağlam; KARA ŞEN, YELİZ; SAĞLAM ÖZKAN, YEŞİM; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-1364-5137; AAG-8304-2021; G-5333-2017In this current work, we introduce a subfamily of analytic functions endowed with k-Pell-Lucas numbers. The radius problems, basic geometric properties and general coefficient relations are obtained for the former class.Publication On the exact solutions to Biswas-Arshed equation involving truncated M-fractional space-time derivative terms(Elsevier, 2021-02-01) Özkan, Yeşim Sağlam; SAĞLAM ÖZKAN, YEŞİM; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-1364-5137; G-5333-2017In this work, two different schemes, the extended hyperbolic auxiliary and the simplest equation method, are employed to construct the exact solutions involving parameters of the Biswas-Arshed model (BAM) with truncated M-fractional derivative. Moreover, semi-inverse variational principle are applied to underlying equation to acquire analytical solution. These methods have a broad applicability to many other nonlinear evolution equations in mathematical physics. Different traveling wave solutions have been investigated by invoking these methods. 3D graphic representations are given to explain the principal effect of parameter mu on dynamical properties of the soliton solutions. The stability property of the obtained solutions is tested to show the ability of our obtained solutions through the physical experiments. Moreover, the general solution of nonlinear ordinary differential equation corresponding to underlying equation is found using traveling wave reduction.Publication On the exact and numerical solutions to a new (2(De Gruyter, 2021-01-01) ; Ozkan, Yesim Saglam; Yasar, Emrullah; Celik, Nisa; SAĞLAM ÖZKAN, YEŞİM; YAŞAR, EMRULLAH; ÇELİK, NİSA; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1364-5137; 0000-0003-4732-5753; ABD-1401-2020; G-5333-2017The aim of this paper is to introduce a novel study of obtaining exact solutions to the (2+1) - dimensional conformable KdV equation modeling the amplitude of the shallow-water waves in fluids or electrostatic wave potential in plasmas. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. By using the improved tan(phi/2)-expansion method (ITEM) and Jacobi elliptic function expansion method, exact solutions including the hyperbolic function solution, rational function solution, soliton solution, traveling wave solution, and periodic wave solution of the considered equation have been obtained. We achieve also a numerical solution corresponding to the initial value problem by conformable variational iteration method (C-VIM) and give comparative results in tables. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.Publication Optical soliton solutions to eight order nonlinear schrodinger equation using some different methods(Springer, 2021-05-01) Yılmaz, Esra Ünal; Özkan, Yeşim Sağlam; SAĞLAM ÖZKAN, YEŞİM; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-1364-5137; G-5333-2017In this study, the eight order nonlinear Schrodinger equation modeling the pulse propagation in optical fiber is discussed. Optical fibers is used for long-distance and high-performance data networking which making it the logical choice for data transmission. For this reason, it becomes important to examine these type equations. Three different useful and effective methods have been used to obtain optical soliton solutions of this equation. In addition, it is tried to give more information about the dynamic performance of the model with the help of three-dimensional graphics. Finally, the stability property of the obtained analytical solution was investigated based on Hamiltonian systems.Publication Pure cubic optical solitons with improved tan(φ/2)-expansion method(Springer, 2021-05-17) Özkan, Yeşim Sağlam; Eslami, Mostafa; Rezazadeh, Hadi; SAĞLAM ÖZKAN, YEŞİM; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1364-5137; G-5333-2017In this paper, we considered the nonlinear Schrodinger equation modeling cubic optical solitons in a polarization-preserving fiber with Kerr law. Using the improved tan(phi/2)-expansion method, a powerful and effective method, we constructed exact solutions including the hyperbolic function solution, the trigonometric function solution, the exponential solution and the rational solution with free parameters. The geometrical shapes for some of the obtained results are depicted for various choices of the free parameters that appear in the results. The obtained solutions are entirely new and can be considered as generalization of the existing results in the ordinary derivative case.Publication The generalized exponential rational function and Elzaki-Adomian decomposition method for the Heisenberg ferromagnetic spin chain equation(World Scientific Publ Co Pte Ltd, 2021-04-30) Özkan, Yeşim Sağlam; SAĞLAM ÖZKAN, YEŞİM; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-1364-5137; G-5333-2017In this paper, the Heisenberg ferromagnetic spin chain equation, which is a model with different magnetic interactions in the classical and semiclassical limits, is investigated using the generalized exponential rational function method. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. A plurality of the exact solution is obtained by using the relevant method. Physical interpretations of some obtained solutions are also included. Particularly, upon choosing appropriate parameters, various plots are depicted. We achieve also a numerical solution corresponding to the initial value problem by the Elzaki-Adomian decomposition method and give comparative results in a table. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.Publication A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws(Pergamon-Elsevier Science Ltd, 2021-02-01) Seadawy, Aly R.; Celik, Nisa; ÇELİK, NİSA; Ozkan, Yesim Saglam; SAĞLAM ÖZKAN, YEŞİM; Yasar, Emrullah; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-7412-4773; 0000-0003-4732-5753; U-1065-2018In this study, we have dealt with a wave equation containing 4th order nonlinear mixed derivative. This model corresponds to solitary waves in nonlinear elastic circular rod. One dimensional optimal systems corresponding to Lie symmetry generator sub-algebras, symmetry reductions, and group invariant solutions corresponding to these systems have been systematically produced by Lie symmetry analysis of this model. In addition, traveling wave solutions were obtained with the help of an useful integration scheme of the model. These solutions are structures with physical properties of hyperbolic, trigonometric and rational solution types. Numerical simulations of the obtained solutions for different values of the parameters were made. The stability property of the obtained solutions is tested to show the ability of obtained solutions. In addition, the local conservation laws of the model were obtained with the help of the multiplier homotopy method.Publication Breather-type and multi-wave solutions for (2+1)-dimensional nonlocal gardner equation(Elsevier, 2021-02-01) Özkan, Yesim Sağlam; Yaşar, Emrullah; Özkan, Yesim Sağlam; SAĞLAM ÖZKAN, YEŞİM; Yaşar, Emrullah; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1364-5137; 0000-0003-4732-5753; G-5333-2017; AAG-9947-2021In this work, different kinds of solutions including breather-type and multi-wave solutions are obtained for the (2 + 1)-dimensional Gardner equation by using bilinear form, the extended homoclinic test approach and three-wave method. We obtained the coefficient conditions in solution ansatz for the existing of breather and multi-wave solutions. By selecting appropriate values of the parameter, three dimensional, contour and density plots of solutions are drawn in order to better understand the dynamic behaviors of considered physical phenomena. (C) 2020 Elsevier Inc. All rights reserved.