Yazar "Daghan, Durmus" seçeneğine göre listele

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    COMPARISON OF (G '/G)-METHODS FOR FINDING EXACT SOLUTIONS OF THE DRINFELD-SOKOLOV SYSTEM
    (WALTER DE GRUYTER GMBH, 2015) Daghan, Durmus; Yildiz, Ozlem; Toros, Serkan
    Nonlinear Drinfeld-Sokolov system is studied analytically by using four different methods (G'/G)-expansion, direct algebraic, different form of the (G'/G)-expansion methods, and direct integration) and the results are found numerically. New exact and numeric solutions are given and the comparison of the results obtained from these different methods, methods themselves and numerical results are discussed in detail. It is found that the (G'/G)-expansion and different form of the (G'/G)-expansion methods are really coincide and effective methods in the view of finding different solutions that cannot be obtained by using the direct integration for Drinfel-Sokolov system.
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    Explicit solutions of the nonlinear partial differential equations
    (PERGAMON-ELSEVIER SCIENCE LTD, 2010) Daghan, Durmus; Donmez, Orhan; Tuna, Adnan
    The convection and diffusion process or their mixed states are the Important phenomena in the different physical systems. In order to understand these physical processes, the nonlinear differential equations, Fisher. Burger-Fisher. Benjamin-Bona-Mahony-Burgers (BBMB) and Modified Benjamin-Bona-Mahony (MBBM) are solved to obtain the traveling wave solutions using (G'/G)-expansion method. In this study we give the exact solutions of these equations which describe the dynamics of turbulence created by the Interaction of matters. Our solutions are reduced to the well-known solutions in the literature assigning some special values to the constants in the solutions of these equations. Moreover, we have reached the new exact solutions for these equations mentioned above. We have also analyzed and plotted the results using different integration constants to understand the behavior of solutions. (C) 2009 Elsevier Ltd. All rights reserved.
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    Generalization of Ostrowski and Ostrowski-Gruss type inequalities on time scales
    (PERGAMON-ELSEVIER SCIENCE LTD, 2010) Tuna, Adnan; Daghan, Durmus
    In this paper, we obtain an Ostrowski and Ostrowski-Gruss type inequality on time scales, which not only provides a generalization of the known results on time scales, but also give some other interesting inequalities as special cases. (C) 2010 Elsevier Ltd. All rights reserved.
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    New exact solutions for the Boiti-Leon-Manna-Pempinelli equation
    (Yildiz Technical Univ, 2024) Yilmaz, Rasime Kubra; Daghan, Durmus
    Phenomena in physics, plasma physics, optical fibers, chemical physics, fluid mechanics, and many fields are often described by the nonlinear evolution equations. The analytical solutions of these equations are very important to understand the evaluation of the physical models. In this paper, the Boiti-Leon-Manna-Pempinelli (BLMP) nonlinear partial differential equation, which can be used to describe the incompressible fluid flow, is analytically studied by using the five different techniques which are direct integration, (G'/G)-expansion method, different form of the (G'/G)-expansion method, two variable (G'/G,1/G)-expansion method, and (1/G')- expansion method. Hyperbolic, trigonometric and rotational forms of solutions are obtained. Our solutions are reduced to the well-known solutions found in the literature by assigning the some special values to the constants appeared in the analytic solutions. Moreover, we have also obtained the new analytic solutions of the BLMP equation.
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    New exact solutions of a nonlinear integrable equation
    (Wiley, 2020) Yildiz, Guldem; Daghan, Durmus
    Analytic solutions of the partial differential equations are needed to explain many phenomena seen in thermodynamics, aerodynamics, plasma physics, and other fields. In this paper, variational principle is analyzed of the integrable nonlinear Korteweg-de Vries (KdV) typed equation. In addition, exact solutions of this equation are obtained by using various methods such as direct integration, homogeneous balance method, Exp-function method, and Kudryashov method.