Browsing by Author "Seadawy, Aly R."
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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 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.Item 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) Seadawy, Aly R.; Çelik, Nisa; Sağlam Özkan, Yeşim; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-1364-5137; ABD-1401-2020; G-5333-2017; AAG-9947-2021; 36005160000; 57193338830; 23471031300In 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. (c) 2020 Elsevier Ltd. All rights reserved.Item Multi-wave, breather and interaction solutions to (3+1) dimensional Vakhnenko–Parkes equation arising at propagation of high-frequency waves in a relaxing medium(Taylor & Francis Ltd, 2021) Seadawy, Aly R.; Sağlam Özkan, Yeşim; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-1364-5137; 0000-0003-4732-5753; AAG-9947-2021; G-5333-2017; 57193338830; 23471031300In this study, based on the Hirota bilinear form, the exact analytic solutions of the (3 + 1) dimensional Vakhnenko-Parkes equation with various physical properties were constructed with the help of the Maple package program and symbolic computation. These solutions are the type of multi-waves, breather wave, lump-kink, lump-periodic solutions and interaction solutions (between lump and hyperbolic wave solutions). The constructed solutions have expanded and enriched the solution forms of this new model existing in the literature. By means of Maple package program, 3D and 2D graphs were drawn for the special choices of the parameters in the solutions, and the physical structures of the solutions obtained in this way were also observed. The solutions obtained can be used in the explanation of physical phenomena occurring in the propagation of high-frequency waves in a relaxing medium.Item On the optical solitons and local conservation laws of Chen-Lee-Liu dynamical wave equation(Elsevier, 2020-08-05) Seadawy, Aly R.; Özkan, Yeşim Sağlam; Yaşar, Emrullah; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1364-5137; 0000-0003-4732-5753; G-5333-2017; AAG-9947-2021; 57220153585; 23471031300In this study, we dealt with the Chen-Lee-Liu equation. This equation models the propagation of soliton flow through optical fibers and other wave-guide mediums. Using the association between Lie point symmetries and local conserved vectors, we extracted some different types of optical soliton solutions of this equation. In addition, we construct the new conservation laws employing the Lie point symmetries of the equation by the approach of Kara and Mahomed.Item Optical solitons and conservation law of Kundu-Eckhaus equation(Elsevier, 2017-10-18) Mirzazadeh, Mohammad; Triki, Houria; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Seadawy, Aly R.; Biswas, Anjan; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 23471031300; 56988856400This paper obtains optical soliton solutions to the Kundu Eckhaus equation with general coefficients. The Riccati Bernoulli's sub-ODE method as well as Kudryashov's scheme are employed to obtain soliton solutions to the model. This generalized earlier reported result of the model with specific coefficients. Subsequently, the multiplier approach was utilized to secure a conserved quantity with the bright soliton solution that was reported earlier.