Abstract:
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.
