Person: YAŞAR, EMRULLAH
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YAŞAR
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EMRULLAH
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Publication On the conservation laws and traveling wave solutions to the bbm equation(Taru Publications, 2010-01-01) Özer, Teoman; Yaşar, Emrullah; YAŞAR, EMRULLAH; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0003-4732-5753; AAG-9947-2021In this study the Benjamin-Bona-Mahony (BBM) equation, modelling long wave motion in nonlinear dispersive systems is discussed. Applying the new general theorem on nonlocal conservation laws [1], (N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., Vol. 333 (2007), pp. 311-328) and using the symmetries of the model equation conservation laws are discussed. Also, we construct reductions and solutions of the BBM equation using inverse variational and symmetry methods.Publication 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; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-6364-3631; 0000-0003-4732-5753; JSK-4572-2023; AAG-9947-2021In 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.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; 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 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; 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 Highly dispersive optical soliton molecules to dual-mode nonlinear Schrodinger wave equation in cubic law media(Springer, 2022-03-01) Kopçasız, Bahadır; Seadawy, Aly R.; Yaşar, Emrullah; Kopcasiz, Bahadir; YAŞAR, EMRULLAH; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-6364-3631; 0000-0003-4732-5753; JSK-4572-2023; AAG-9947-2021In the manuscript under investigation, the dual-mode form of nonlinear Schr odinger equation was examined. This model is used for studying the enlargement or absorption of dual waves in the occurrence of nonlinearity and distribution effects. Bright, dark, combined bright-dark, singular soliton, periodic, rational and solitary wave solutions of this equation are obtained. Preferred integration schemes are the extended (G'/G), sine-cosine, and semi-inverse methods. Numerical simulations of the obtained solutions were carried out for the special values of the parameters in the solutions and 3D and contour graphs were drawn. The convergence analysis of the performed schemas to the model were also demonstrated.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; 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 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; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-6364-3631; 0000-0003-4732-5753; JSK-4572-2023; AAG-9947-2021This 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).Publication Optical soliton solution analysis for the (2+1) dimensional kundu-mukherjee-naskar model with local fractional derivatives(Springer, 2022-07-01) San, Sait; Seadawy, Aly R.; Yaşar, Emrullah; YAŞAR, EMRULLAH; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0003-4732-5753; AAG-9947-2021In this paper, we investigate the local fractional Kundu-Mukherjee-Naskar (LFKMN) equation in (2+1) dimensional case. The Yang's local fractional calculus tool has fulfilled a significant character in defining the fractal behaviours in a fractal space or microgravity space that arise in applied nonlinear sciences. The travelling wave transformation of the non-differentiable type is introduced and we retrieve successfully the non-differentiable exact traveling wave solutions (soliton pulses in (2+1)-dimensions) of LFKMN equation with aid of generalized exp-function method in the form of generalized functions described on Cantor sets. With the help of Mathematica package program, 3D graphs were drawn for the special values 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 propagation of rogue waves in oceans and higher order optical solitons in optical fibers in current-like nonlinearities.The deduced explicit solutions will cause a new pathway of the nonlinear wave theory by the help of local fractional derivative. The proposed approach is demostrated to ensure a beneficial tool to solve the local fractional nonlinear evolution equations in applied nonlinear sciences.Publication Variational operators, symplectic operators, and the cohomology of scalar evolution equations(Springernature, 2019-06-04) Fels, M. E.; Yaşar, E.; YAŞAR, EMRULLAH; 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 Multi wave, kink, breather, interaction solutions and modulation instability to a conformable third order nonlinear schrodinger equation(Springer, 2023-04-01) Ay, Nursena Günhan; GÜNHAN, NURSENA; Yaşar, Emrullah; YAŞAR, EMRULLAH; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-1919-2431; 0000-0003-4732-5753; HNT-0160-2023; HOC-4413-2023The purpose of this work is the examine the three-waves, double exponential, homoclinic breather, and periodic cross kink-soliton solutions for a third-order fractional nonlinear Schrodinger equation (3-FNLS). This model which is vital in fiber optics, explains the propagation of light in optical fibers when ultra-short pulses are produced. We define the model in terms of the conformable time fractional derivative operator so that the model could give a better description of the physical aspect. By picking the activation function in Hirota bilinear form, as the hyperbolic, trigonometric and exponential function along with suitable dispose of parameters, we acquire the three-waves, double exponential, homoclinic breather, and periodic cross kink-soliton auspiciously. Additionally, we have elucidated some three-dimensional and contour portraits to foresee the wave dynamics. These acquired new solutions that do not exist in the literature include some free constants and thereby can be significant to describe variety in qualitative aspects of wave phenomena. At last, we also check the stability of the governing model. By executing the modulation instability analysis, we scrutinize the stability analysis of the yielded exact solutions and the movement role of the waves.
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