Browsing by Author "Akbulut A., Kaplan M., Kaabar M.K.A."

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    New conservation laws and exact solutions of the special case of the fifth-order KdV equation
    (2022-08-01) Akbulut A., Kaplan M., Kaabar M.K.A.; Akbulut, A, Kaplan, M, Kaabar, MKA
    The current study deals with the Kaup-Kupershmidt (KK) equation to construct formal Lagrangian, conservation laws, and exact solutions. KK is basically a special case of the 5th-order KdV equation. The conservation laws obtained by using the conservation theorem are trivial conservation laws. In addition, exact solutions are found via the modified simple equation (MSE) method. For a suitable value of solutions, the 3D surfaces have been plotted using MAPLE. These plots giving novel exact solutions are made to reveal important wave characteristics. Our obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.
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    New exact solutions of the Mikhailov-Novikov-Wang equation via three novel techniques
    (2023-01-01) Akbulut A., Kaplan M., Kaabar M.K.A.; Akbulut, A, Kaplan, M, Kaabar, MKA
    The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different techniques. The adopted methods are generalized Kudryashov method (GKM), exponential rational function method (ERFM), and modified extended tanh-function method (METFM). Some plots of some presented new solutions are represented to exhibit wave characteristics. All results in this work are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in ocean engineering and physics. This equation provides new insights to understand the relationship between the integrability and water waves’ phenomena.