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    Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique
    (Springer, 2020) Gao, Wei; Rezazadeh, Hadi; Pınar, Zehra; Baskonus, Haci Mehmet; Sarwar, Shahzad; Yel, Gülnur
    This paper presents an analytical solver which is known as a generalization of types methodologies. With the proposed method, one of the old but at the same time popular problem is considered, which is known as nonlinear Zoomeron equation, and its analytical solutions are tried to obtain. Moreover, the known solutions, many new analytical solutions are obtained via the proposed method. Plotting some simulations of the solutions, we can present a conclusion.
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    On the Hermite and Mathieu Special Characterizations to the Logarithmic Zakharov–Kuznetsov Equations
    (Springer, 2024) Pinar, Zehra; Baskonus, Haci Mehmet; Veeresha, P.; Gao, Wei
    In this paper, we find the new travelling wave solutions for several aspects of logarithmic Zakharov–Kuznetsov (ZK) equations using an efficient technique called the special function method which is composed of Hermite and Mathieu differential equations being novel and special functions. In order to illustrate the efficiency of the projected scheme, we considered four different examples with different cases, namely, logarithmic ZK (log-ZK) equation, logarithmic modified ZK (log-mZK) equation, and logarithmic ZK modified equal width (log-ZK-mEW) equation and logarithmic ZK–Benjamin–Bona–Mahony (log-ZKBBM) equation. The behaviour of the obtained results and corresponding consequences are illustrated and captured. Finally, the obtained results confirm that the considered solution procedure can be widely employed to find the solution and also capture some interesting and stimulating consequences. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.