Yazar "Kaya, Dogan" seçeneğine göre listele

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    Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method
    (Elsevier, 2022) Iskenderoglu, Gulistan; Kaya, Dogan
    In this work, we present an application of Lie group analysis to study the generalized derivative nonlinear Schrodinger ¨ equation, which governs the evolution of a nonlinear wave and plays an important role in the propagation of short pulses in optical fiber systems. To construct Lie group reductions, we study the symmetry properties and introduce various infinitesimal operators. Further, we obtain self-similar solutions and periodic soliton solutions of the generalized derivative nonlinear Schrodinger ¨ equation. This type of solution plays a vital role in the study of the blow-up and asymptotic behavior of non-global solutions. And at the end, we present graphs for each solution by considering the physical meaning of the solutions.
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    Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2020) Yokus, Asif; Kaya, Dogan
    The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Backlund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier-von Neumann stability analysis, the stability of the FDM with the cKdV-mKdV equation is analyzed. The L-2 and L-infinity norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.
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    An expansion method for generating travelling wave solutions for the (2 + 1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients
    (Elsevier, 2024) Yokuş, Asıf; Duran, Serbay; Kaya, Dogan
    This paper presents a new approach to studying nonlinear evolution equations with variable coefficients and applies it to the Bogoyavlensky-Konopelchenko equation. The Bogoyavlensky-Konopelchenko equation, which describes the interaction between a long wave and a Riemann wave in a special fluid, has many applications in fluid dynamics of mathematical physics. Most studies in the literature focus on the Bogoyavlensky Konopelchenko equation with constant coefficients. This can lead to deficiencies in the understanding of the physical phenomena revealed by the model. To overcome this limitation, terms with time-varying coefficients are introduced into the Bogoyavlensky-Konopelchenko equation. With the addition of these terms, the model is brought closer to the real problem and the physical phenomenon can discussed with more freedom. This study has three main focal points. Firstly, it introduces a novel approach designed for nonlinear evolution equations characterized by variable coefficients. Secondly, the proposed method is applied to generate solutions for the Bogoyavlensky-Konopelchenko equation, showcasing distinctions from existing literature. Finally, the effects of time-varying coefficients on solitons and their interactions with each other in the generated travelling wave solutions are analysed in detail under certain restrictive conditions. The results shed light on the physical behavior of the Bogoyavlensky-Konopelchenko equation with variable coefficients and contribute to a better understanding of similar models. The proposed method opens new possibilities for the study of nonlinear evo lution equations with variable coefficients and provides avenues for analytical investigation of their solutions.
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    A new approach for Painlevé analysis of the generalized Kawahara equation
    (American Institute of Physics Inc., 2015) Kutlu, Busra; Kaya, Dogan
    In this paper, generalized Kawahara equation with a source is considered. It is shown that this equation is nonintegrable by using Painlevé test. An exact solution is also obtained with the help of simplified Hirota's method for the considered equation. © 2015 AIP Publishing LLC.
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    New Wave Solutions for Nonlinear Differential Equations using an Extended Bernoulli Equation as a New Expansion Method
    (E D P Sciences, 2018) Duran, Serbay; Kaya, Dogan
    In this paper, we presented a new expansion method constructed by taking inspiration for the Kudryashov method. Bernoulli equation is chosen in the form of F' = BFn AF and some expansions are made on the auxiliary Bernoulli equation which is used in this method. In this auxiliary Bernoulli equation some wave solutions are obtained from the shallow water wave equation system in the general form of n-order. The obtained new results are simulated by graphically in 3D and 2D. To sum up, it is considered that this method can be applied to the several of nonlinear evolution equations in mathematics physics.
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    ON LIE GROUP ANALYSIS OF BOUNDARY VALUE PROBLEM WITH CAPUTO FRACTIONAL DERIVATIVE
    (YILDIZ TECHNICAL UNIV, 2019) Iskenderoglu, Gulistan; Kaya, Dogan
    Lie symmetry analysis of initial and boundary value problem for partial differential equations with Caputo fractional derivative is investigated. Also given generalized definition and theorem for symmetry method for partial differential equation with Caputo fractional derivative. The group symmetries and examples on reduction of fractional partial differential equations with initial and boundary conditions to nonlinear ordinary differential equations with initial condition are present.
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    Role of Gilson-Pickering equation for the different types of soliton solutions: a nonlinear analysis
    (SPRINGER HEIDELBERG, 2020) Yokus, Asif; Durur, Hulya; Abro, Kashif Ali; Kaya, Dogan
    In this article, the soliton solutions of the Gilson-Pickering equation have been constructed using the sinh-Gordon function method (ShGFM) and (G '/G, 1/G)-expansion method, which are applied to obtain exact solutions of nonlinear partial differential equations. A solution function different from the solution function in the classical (G '/G, 1/G)-expansion method has been considered which are based on complex trigonometric, hyperbolic, and rational solutions. By invoking ShGFM and (G '/G, 1/G)-expansion methods, different traveling wave solutions have been investigated. For the sake of avoiding the complex calculations, the ready package program has been tackled. The comparative analysis of sinh-Gordon function and (G '/G, 1/G)-expansion methods has shown several differences and similarities. A comparative analysis of ShGFM and (G '/G, 1/G)-expansion methods assures that the (G '/G, 1/G)-expansion method has been found to be more intensive, powerful, reliable and effective method for the Gilson-Pickering equation. The graphical illustrations of two-, three-dimensional, and contour graphs have been depicted as well.
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    Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense
    (PERGAMON-ELSEVIER SCIENCE LTD, 2020) Iskenderoglu, Gulistan; Kaya, Dogan
    In this work, we study Lie symmetry analysis of initial and boundary value problems (IBVPs) for partial differential equations (PDE) with Caputo fractional derivative. According to Bluman's definition and theorem for the symmetry analysis of the PDE system, we determine the symmetries of the PDE with Caputo fractional derivative in general form and prove theorem for the above equation. We investigate the symmetry analysis of IBVP for a fractional diffusion and third-order fractional partial differential equation (FPDE). And as a result of applying the method, we get several solutions. (C) 2020 Elsevier Ltd. All rights reserved.