A diversity of patterns to new (3

This article discusses the behavior of specific dispersive waves to new (3+1)-dimensional Hirota bilinear equation (3D-HBE). The 3D-HBE is used as a governing equation for the propagation of waves in fluid dynamics. The Hirota bilinear method (HBM) is successfully applied together with various test strategies for securing a class of results in the forms of lump-periodic, breather-type, and two-wave solutions. Solitons for nonlinear partial differential equations (NLPDEs) can be identified via the well-known mathematical methodology known as the Hirota method. However, this requires for bilinearization of nonlinear PDEs. The method employed provides a comprehensive explanation of NLPDEs by extracting and also generating innovative exact solutions by merging the outcomes of various procedures. To further illustrate the impact of the parameters, we also include a few numerical visualizations of the results. These findings validate the usefulness of the used method in improving the nonlinear dynamical behavior of selected systems. These results are used to illustrate the physical properties of lump solutions and the collision-related components of various nonlinear physical processes. The outcomes demonstrate the efficiency, rapidity, simplicity, and adaptability of the applied algorithm.

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This article discusses the behavior of specific dispersive waves to a new (3+1)-dimensional Hirota bilinear equation (3D-HBE) and demonstrates a comprehensive explanation of nonlinear partial differential equations using the Hirota method. It also showcases the efficiency and adaptability of the employed algorithm.