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YAŞAR, EMRULLAH

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YAŞAR

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EMRULLAH

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2010 - 2019102020 - 202319
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Now showing 1 - 10 of 29
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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-9947-2021
    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.
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    Analytical soliton solutions of the fractional order dual-mode nonlinear schrodinger equation with time-space conformable sense by some procedures
    (Springer, 2023-07-01) Kopcasız, Bahadır; Yaşar, Emrullah; Kopcasız, Bahadır; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-6364-3631; 0000-0003-4732-5753; JSK-4572-2023; AAG-9947-2021
    This paper considers the fractional order dual-mode nonlinear Schrodinger equation (FDMNLSE) with cubic law nonlinearity. The FDMNLSE interprets the concurrent propagation of two-mode waves instead of a single wave. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. The FDMNLSE introduces three physical parameters: dispersive factor, phase speed, and nonlinearity. This new model has many applications in nonlinear physics and fiber optics. We will use two methods to get new optical solutions: the generalized exponential rational function method (GERFM) and the functional variable method (FVM). Using the GERFM, we get unique wave solutions in the forms of shock wave solutions, singular soliton solutions, singular periodic waves, and exponential function solutions. Thanks to FVM, we reach bright optical soliton solutions, singular optical soliton solutions, and periodic singular wave solutions, and the restraint conditions for solutions are reported. The analytical outcomes are supplemented with numerical simulations of the got solutions to understand the dynamic behavior of obtained solutions. The results of this study may have a high-importance application while handling the other nonlinear partial differential equations (NLPDEs).
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    Novel multiple soliton and front wave solutions for the 3D-vakhnenko-parkes equation
    (World Scientific, 2022-03-30) Özkan, Yeşim Sağlam; Yaşar, Emrullah; Osman, M. S.; SAĞLAM ÖZKAN, YEŞİM; YAŞAR, EMRULLAH; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-1364-5137; 0000-0003-4732-5753; G-5333-2017; AAG-9947-2021
    The multiple exp-function technique, as an extension to Hirota's perturbation algorithm, is employed to find N-soliton solutions of the 3D Vakhnenko-Parkes (3D-VP) equation. This is a straightforward and effective alternative method. Consequently, one- two- and three-soliton solutions besides the front wave solutions and their wave numbers are obtained, which are completely distinct from the other published literature. 3D and density plots were investigated via the help of the Maple package program by suitably choosing the free parameters in the solutions. Further, the physical meaning for these solutions is clarified. We mention that the propagation of high-frequency waves in a relaxing medium can be investigated by discussing the dynamical behavior of the obtained solutions for the 3D-VP equation.
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    On the lie symmetry analysis, analytic series solutions, and conservation laws of the time fractional belousov-zhabotinskii system
    (Springer, 2022-06-03) San, Sait; Yaşar, Emrullah; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0003-4732-5753
    In this study, a reaction mechanism proposed by Belousov and Zhabotinskii, which corresponds to many physical phenomena, from the complex wave behavior of the heart and various organs in our body to the formation of biological models that cause embryonic developments, was examined. We considered the derivative with the time evolution as the Riemann-Liouville derivative operator. Lie symmetry generators corresponding to the transformation groups in which our model remains invariant were constructed. The power series solution was systematically designed, including the convergence analysis of this system. Besides, conservation laws of the model were created for the 0 < alpha < 1 states of the a fraction order.
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    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-9947-2021
    The 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.
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    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-9875-2023
    In 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.
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    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-9947-2021
    For 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.
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    On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation
    (Elsevier, 2015-05-01) Şan, Sait; Yaşar, Emrullah; YAŞAR, EMRULLAH; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-4732-5753; AAG-9947-2021
    In this study, the nonlocal conservation theorem and multiplier approach are performed on the 1 + 1 dimensional Derrida-Lebowitz-Speer-Spohn (DLSS) equation which arises in quantum semi conductor theory. We obtain local conservation laws by using the both methods. Furthermore by utilizing the relationship between conservation laws and Lie point symmetries, the DLSS equation is reduced to third order ordinary differential equation.
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    The investigation of unique optical soliton solutions for dual-mode nonlinear schrodinger's equation with new mechanisms
    (Springer, 2022-11-23) Kopçasız, Bahadır; Yaşar, Emrullah; Kopçasız, Bahadır; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-6364-3631; 0000-0003-4732-5753; JSK-4572-2023; AAG-9947-2021
    In this study, we regard the dual-mode nonlinear Schrodinger equation (DMNLSE). The DMNLSE depicts the propagations of two-moving waves synchronically. The extended rational sine-cosine and sinh-cosh methods under the homogeneous balance principle are employed for obtaining solutions. Different types of optical solitons are obtained. These solutions are new solutions for the DMNLSEs that are not reported by the other methods. The properties are displayed with figures for these solutions. Moreover, the stability analysis is also discussed. The obtained outcomes demonstrate that these structure methods are straightforward, efficient, brief and can be used in better complex phenomena with the help of symbolic computations.
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    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-9875-2023
    In 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.