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ÇELİK, NİSA

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ÇELİK

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    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-5333-2017
    The 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.
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    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-9947-2021
    In 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.
  • No Thumbnail Available
    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-1065-2018
    In 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.