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    Application of some nonclassical methods for p-defocusing complex Klein–Gordon equation
    (Springer, 2023) Yokuş, Asif; İskenderoğlu, Gülistan; Kaya, Doğan
    This research studies the high-energy Klein–Gordon equation, related to the relativistic Schrödinger wave equation. Solutions are produced using the Kudryashov transform and conventional wave transform. The study’s most significant finding is the examination of the physical and mathematical differences in the traveling wave solutions, derived using two alternative transformations. The graphs of the intensity of the wave function and the conclusions at various velocity levels are also examined. The stability analysis of the moving waves, which coincides with Graham’s diffusion law, of the relationship between wave velocity and density is examined and its relationship with the propagation equation is investigated.
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    Conservation laws and a new expansion method for sixth order Boussinesq equation
    (American Institute of Physics Inc., 2015) Yokuş, Asif; Kaya, Doğan
    In this study, we analyze the conservation laws of a sixth order Boussinesq equation by using variational derivative. We get sixth order Boussinesq equation's traveling wave solutions with (1/G)-expansion method which we constitute newly by being inspired with (G/G)-expansion method which is suggested in [1]. We investigate conservation laws of the analytical solutions which we obtained by the new constructed method. The analytical solution's conductions which we get according to new expansion method are given graphically. © 2015 AIP Publishing LLC.
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    Numerical solutions of the Fractional Kdv-Burgers-Kuramoto equation
    (Serbian Society of Heat Transfer Engineers, 2018) Kaya, Doğan; Gülbahar, Sema; Yokuş, Asif
    Non-linear terms of the time-fractional KdV-Burgers-Kuramoto equation are linearized using by some linearization techniques. Numerical solutions of this equation are obtained with the help of the finite difference methods. Numerical solutions and corresponding analytical solutions are compared. The 2 L and L8 error norms are computed. Stability of given method is investigated by using the Von Neumann stability analysis. © 2018 Society of Thermal Engineers of Serbia.
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    Solutions of the fractional combined KdV-mKdV equation with collocation method using radial basis function and their geometrical obstructions
    (Springeropen, 2018) Kaya, Doğan; Gülbahar, Sema; Yokuş, Asif; Gülbahar, Mehmet
    The exact solution of fractional combined Korteweg-de Vries and modified Korteweg-de Vries (KdV-mKdV) equation is obtained by using the expansion method. To investigate a geometrical surface of the exact solution, we choose . The collocation method is applied to the fractional combined KdV-mKdV equation with the help of radial basis for . and error norms are computed with the Mathematica program. Stability is investigated by the Von-Neumann analysis. Instable numerical solutions are obtained as the number of node points increases. It is shown that the reason for this situation is that the exact solution contains some degenerate points in the Lorentz-Minkowski space.