Yazar "Duran, Serbay" seçeneğine göre listele

Listeleniyor 1 - 9 / 9
  • Küçük Resim Yok
    Öğe
    Applications of a new expansion method for finding wave solutions of nonlinear differential equations
    (2012) Duran, Serbay; Kaya, Doğan
    In this paper, we presented a new expansion method constructed by taking inspiration for the Kudryashov method. Bernoulli equation was chosen in the form of F' = FB n-AF and made some expansions on the auxiliary Bernoulli equation which used in this method. In this auxiliary Bernoulli equation, by taking n = 3, some wave solutions obtained from Burgers equation and the shallow water wave equation system. As a result, for special values, we concludedthree dimensional wave views for solutions of Burgers Equation and the shallow water wave equation system.To sum up, it is considered that this method can be applied to other nonlinear evolution equations in mathematics physics. © IDOSI Publications, 2012.
  • Küçük Resim
    Öğe
    Applications of the sub equation method for the high dimensional nonlinear evolution equation
    (Erzincan Binali Yıldırım Üniversitesi, Fen Bilimleri Enstitüsü, 2021) Duran, Serbay; Kaya, Doğan
    In this article, the Generalized (3+1)-dimensional Shallow Water-Like (SWL) equation is taken into consideration and exact solutions have been constructed of the SWL equation using sub equation method. This method is an easier and efficient method for finding analytic solutions of the nonlinear evolution differential equation. The method appears to be easier and faster for symbolic computation. Moreover, 2D, 3D and contour graphical representation of the obtained results of the specified equation is made using a ready-made package program for certain values and thus the conformity of the founded results has been demonstrated.
  • Küçük Resim
    Öğe
    Breaking analysis of solitary waves for the shallow water wave system in fluid dynamics
    (Springer, 2021) Duran, Serbay; Kaya, Doğan
    Analytical solutions and physical interpretations for the shallow water wave system, which is the modeling of a physical phenomenon in applied mathematics, are presented in this study. The solutions of the shallow water wave system, which models the formation, interaction and breaking of shallow water waves on the ocean surface as a result of external effects (e.g., wind), are examined using the modified expansion method. Besides, physically, the differences between deep and shallow water waves and their transitions with each other are examined. Hyperbolic and trigonometric wave solutions are produced with the advantages of the modified expansion method over other traditional methods. In these wave solutions, the values that cause the breaking of the wave are calculated by considering the velocity parameter. The behavior of the wave at these values is presented with the help of simulations. Finally, the states of solitary wave solutions concerning each other in the same system are compared and analyzed according to the velocity parameter.
  • Küçük Resim
    Öğe
    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.
  • Küçük Resim Yok
    Öğe
    Investigation of exact soliton solutions of nematicons in liquid crystals according to nonlinearity conditions
    (World Scientific, 2023) Durur, Hülya; Yokuş, Asıf; Duran, Serbay
    In this work, new traveling wave solutions are generated for the system that models nematicons in liquid crystals using the (1/G?)-expansion method. In the equation system, nonlinearity is taken into account for Kerr law and Power law. Also, the existence of exact solutions under restriction conditions is guaranteed. We suggest that the solutions produced are of a different type than the solutions in the literature. Figures representing the intensity of the produced traveling wave solutions are presented. In addition, the simulation of the solitary wave is made for different values of the parameter that affects the inclination angle of the molecules in the nematicons mechanism in liquid crystals. How classical solitary wave behavior translates into triangular wave behavior is discussed. We believe this paper will provide an important perspective on the problems encountered in various application areas such as fluid dynamics, chemical engineering, chaos and complex networks in terms of investigating different mechanisms by taking into account nonlinearity factors.
  • Küçük Resim Yok
    Öğe
    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.
  • Küçük Resim Yok
    Öğe
    Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics
    (World Scientific, 2021) Duran, Serbay; Yokuş, Asıf; Durur, Hülya; Kaya, Doğan
    In this study, the modified (1/G?)-expansion method and modified sub-equation method have been successfully applied to the fractional Benjamin–Ono equation that models the internal solitary wave event in the ocean or atmosphere. With both analytical methods, dark soliton, singular soliton, mixed dark-singular soliton, trigonometric, rational, hyperbolic, complex hyperbolic, complex type traveling wave solutions have been produced. In these applications, we consider the conformable operator to which the chain rule is applied. Special values were given to the constants in the solution while drawing graphs representing the stationary wave. By making changes of these constants at certain intervals, the refraction dynamics and physical interpretations of the obtained internal solitary waves were included. These physical comments were supported by simulation with 3D, 2D and contour graphics. These two analytical methods used to obtain analytical solutions of the fractional Benjamin–Ono equation have been analyzed in detail by comparing their respective states. By using symbolic calculation, these methods have been shown to be the powerful and reliable mathematical tools for the solution of fractional nonlinear partial differential equations.
  • Küçük Resim Yok
    Öğe
    A study on solitary wave solutions for the Zoomeron equation supported by two-dimensional dynamics
    (IOP Publishing Ltd, 2023) Duran, Serbay; Yokus, Asif; Kilinc, Gulsen
    This study emphasizes the importance of understanding natural phenomena through various observations and relating them to scientific studies. Nonlinear partial differential equations serve as fundamental tools for modeling these phenomena, with a focus on nonlinear evolution equations when involving time. This paper investigates the dynamics of the Zoomeron equation, highlighting not only a result derived from the KdV and Schrodinger equations but also its contribution to the modeling of Boomeron and Trappon solitons. Different analytical techniques yield various solutions for the Zoomeron equation, each offering unique insights. The behavior of the solutions generated in kink and singular soliton forms in various dynamics using the G'/G(2) -expansion method is investigated and compared under restrictive conditions, and the distribution of energy density is explained with the assistance of the gradient function. It is aimed at gaining a physically unique perspective by revealing the connections between the velocities of solitons produced for this equation and the effects of gradient flow directions. In addition, stability analysis for some of the solutions generated in the kink form is investigated. The structure of the paper includes method introduction, application, stability property, results and discussion, resulting in a unique perspective on understanding the physical dynamics of the Zoomeron model.
  • Küçük Resim
    Öğe
    Traveling wave and general form solutions for the coupled Higgs system
    (John Wiley & Sons Ltd., 2023) Duran, Serbay; Durur, Hülya; Yokuş, Asıf
    In this study, the coupled Higgs system, which is a special case of the coupledHiggs field equation, which is effective in energy transport in the sub-particlesof the atom, is discussed. With the help of the modified generalized exponen-tial rational function method, which is an important instrument in obtainingtraveling wave solutions, both the propagating wave solutions and generalform solutions of coupled Higgs system are presented. These solutions areexamined under some restrictive conditions as they are presented. It is arguedthat these solutions differ from the literature. The advantages and disadvan-tages of the method discussed in the conclusion and discussion section are dis-cussed. In addition, the changes in the behavior of the traveling wave solutionare discussed by giving physical meaning to some constants in the travelingwave solutions produced by the method. The effects on the traveling wavesolution are analyzed for different values of wave number, wave velocity, andwave frequency, which have physically important meanings. In addition, thebehaviors caused by these effects are supported with the help of simulation.