Person: YAŞAR, EMRULLAH
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YAŞAR
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EMRULLAH
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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 Soliton solutions to the non-local boussinesq equation by multiple exp-function scheme and extended kudryashov's approach(Indian Acad Sciences, 2019-02-01) Adem, Abdullahi Rashid; Yıldırım, Yakup; Yaşar, Emrullah; Yıldırım, Yakup; YAŞAR, EMRULLAH; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-4443-3337; 0000-0003-4732-5753; AAG-9947-2021; HTO-9875-2023In this paper, we study the exact solutions of non-local Boussinesq equation (nlBq) which appears in many scientific fields. We generate dark solitons, singular solitons, a new family of solitons and combo dark-singular soliton-type solutions of nlBq by the extended Kudryashov's algorithm. Additional solutions such as singular periodic solutions also fall out of this integration scheme. Also, one-soliton, two-soliton and three-soliton type solutions are presented using multiple exp-function algorithm. Lastly, Lie symmetry analysis with the new similarity reductions is also examined.Publication The logarithmic (1+1)-dimensional KdV-like and (2+1)-dimensional KP-like equations: Lie group analysis, conservation laws and double reductions(Gmbh, 2019-12-01) Giresunlu, İlker Burak; Yaşar, Emrullah; Adem, Abdullahi Rashid; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAG-9947-2021We investigate the logarithmic (1 + 1) dimensional KdV-like and (2 + 1) dimensional KP-like equations which model many physical processes in the field of soliton theory. In this paper, first, we get the classical Lie point symmetries using the invariance theory. Secondly, we obtain conservation laws of the underlying equations by incorporating the method of multiplier and non-local conservation method. A relationship between the obtained symmetries and conservation laws are shown. Then using the generalized double reduction theory for the associated symmetries, reductions are constructed. Finally traveling wave solutions are computed with the aid of the simplest equation method for the logarithmic (2 + 1)-dimensional KP-like equation.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 perturbation in parabolic law medium having weak non-local nonlinearity by a couple of strategic integration architectures(Elsevier, 2019-06-01) Biswas, Anjan; Yıldırım, Yakup; Yaşar, Emrullah; Zhou, Qin; Alshomrani, Ali Saleh; Belic, Milivoj; Yıldırım, Yakup; YAŞAR, EMRULLAH; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-4443-3337; 0000-0003-4732-5753; AAG-9947-2021; HTO-9875-2023In this paper, the governing model with the inclusion of parabolic law nonlinearity, weakly non-local nonlinearity in addition to perturbation terms is examined for the sake of uncovering quite important optical soliton solutions. Dark, bright and singular solitons in addition to singular periodic solutions are yielded with the modified simple equation technique and trial equation architecture along with parameter restrictions.Publication Variational operators, symplectic operators, and the cohomology of scalar evolution equations(Springernature, 2019-06-04) Fels, M. E.; Yaşar, E.; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021For a scalar evolution equation u(t) = K(t, x, u, u(x), . . . , u(2m+1)) with m >= 1, the cohomology space H-1,H-2() is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for u(t) = K for which the equation is Hamiltonian is also shown to be isomorphic to the space H-1,H-2() and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest.Publication Optical soliton solutions to a (2+1) dimensional Schrodinger equation using a couple of integration architectures(Walter, 2021-01-01) Çankal, Pelin Doğan; Yaşar, Emrullah; Çankal, Pelin Doğan; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-4732-5753; CGW-4502-2022; AAG-9947-2021In this work, we consider a (2+1) dimensional nonlinear Schrodinger system which appears in the theory of nonlinear optics and describe transmission of the optical pulses in optical fibers. We attain certain special type traveling wave solutions of the under investigated model by help of finite series expansion and auxiliary differential equations. In this manner, we exploit exp(-phi(epsilon)) and modified Kudryashov approaches as solution procedures. Moreover, we make tanh ansatz because of the being even order of the reduced ordinary differential equation. The obtained solutions are in the form of dark soliton, combined soliton, symmetrical Lucas sine, Lucas cosine functions, and periodic wave solutions. We present also some graphical simulations of the solutions corresponding to values of parameters which leads to a better understanding the phenomena.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.