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    New Optical Solitons for Time Fractional Coupled Zakharov Equations
    (Springer, 2022) Inc, M.; Ouahid, L.; Owyed, S.; Abdou, M.A.; Abdel-Baset, A.M.; Akgül, A.
    Here, new methods called the expa function and Kudryashov methods are implemented to obtain the analytical solutions of the fractional Zakharov system. The techniques have been taken to execute this aim in a straightforward method. A vast variety of the apparent exact solutions are obtained. Simulations have been demonstrated to prove the efficiency of the proposed techniques. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    Numerical discretization for Fisher-Kolmogorov problem with nonlocal diffusion based on mixed Galerkin BDF2 scheme
    (Elsevier B.V., 2024) Manimaran, J.; Shangerganesh, L.; Zaky, M.A.; Akgül, A.; Hendy, A.S.
    Nonlocal problems involving fourth-order terms pose several difficulties such as numerical discretization and its related convergences analysis. In this paper, the well-posedness of the extended Fisher-Kolmogorov equation with nonlocal diffusion is first analyzed using the Faedo-Galerkin technique and the classical compactness arguments. Moreover, we adopt a BDF2 scheme for time discretization and a mixed Galerkin scheme for spatial discretization. Then, we derive the optimal order convergence rates of the fully discrete system. Finally, some numerical simulations and convergence results are provided to confirm the theoretical results and the accuracy of the proposed scheme. © 2024 IMACS
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    The positive multi-complexiton solution to a generalized Kadomtsev–Petviashvili equation
    (Elsevier B.V., 2024) Hosseini, K.; Hincal, E.; Sadri, K.; Rabiei, F.; Ilie, M.; Akgül, A.; Osman, M.S.
    Recently, Lin et al. (Appl. Math. Lett. 78 (2018) 112–117) established the resonant multiple-wave solution of a generalized Kadomtsev–Petviashvili (gKP) equation with applications in applied sciences using the linear superposition technique. In the present paper, according to the results obtained by Lin et al. and adopting a systematic method established by Zhou and Manukure, the positive multi-complexiton solution to the generalized Kadomtsev–Petviashvili equation is constructed for the first time. Several simulations in three dimensions are conducted formally in order to examine the dynamic behavior of positive multi-complexiton solutions, particularly the positive single-, double-, and triple-complexion waves. The current research outcomes definitely will enrich studies related to the gKP equation and its exact solutions. © 2024