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In this article, we discuss the wave behavior to the (3+1)-dimensional dynamical nonlinear model which models the waves in the shallow water. Some natural issues, including tides, storms, atmospheric flows, and tsunamis, are associated with shallow water waves. Long water waves, also known as shallow water waves, are water waves that have a large water wavelength in relation to their depth. The Hirota bilinear method (HBM) together with different test functions is used to secure the diversity of wave structures. The Hirota method is a well-known and reliable mathematical tool for finding soliton solutions of nonlinear partial differential equations (NLPDEs) in many fields, such as mathematical physics, nonlinear dynamics, oceanography, engineering sciences, and others. However, it demands bilinearization of nonlinear PDEs. The solutions in different kinds such as breather-type, lump-periodic, rouge waves and two wave solutions are extracted. NLPDEs are well-explained by the applied technique since it offers previously derived solutions and also extracts new exact solutions by incorporating the results of multiple procedures. Moreover, in explaining the physical representation of certain solutions, we also plot 3D, 2D, and contour graphs using the corresponding parameter values. This paper’s findings can enhance the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the employed methodology. We believe that a large number of specialists in engineering models will benefit from this research. The results indicate that the employed algorithm is effective, swift, concise, and applicable to complex systems. |
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