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    Öğe
    Novel Exact and Solitary Wave Solutions for The Time-Fractional Nonlinear Maccari's System
    (Universal Wiser Publisher, 2023) Gasmi, Boubekeur; Alhakim, Lama; Mati, Yazid; Moussa, Alaaeddin; Akgul, Ali; Wannan, Rania; Asad, Jihad
    The purpose of this research is to find analytical solutions to the time-fractional nonlinear Maccari system. The double auxiliary equation method, which has never been used before, is used to obtain these solutions. The method is cleverly applied, resulting in the generation of nine new exact solitary wave solutions that have never been found before. We also describe the system's dynamic behavior and the bifurcation of traveling waves. Finally, we show some solutions with different coefficient values that correspond to the nine discovered solutions graphically.
  • [ X ]
    Öğe
    Solving nonlinear partial differential equations using a novel Cham method
    (Taylor & Francis Ltd, 2023) Gasmi, Boubekeur; Moussa, Alaaeddin; Mati, Yazid; Alhakim, Lama; Akguel, Ali
    Nonlinear partial differential equations (NLPDEs) have been of great interest in recent years due to their numerous applications. While there are several methods for finding exact solutions to various NLPDEs, more solutions are still required. This paper first proposes the Cham method, a new method for solving NLPDEs that can generate eight families of solutions. The method is then successfully employed to solve the (2+1)-dimensional Bogoyavlenskii's breaking soliton equations. The dynamic behaviour of these equations and the bifurcation of traveling waves are also discussed. Finally, we graphically depict some solutions corresponding to some discovered solutions with different coefficient values. The Cham method is general, effective, and adaptable to many NLPDEs.