On the interaction phenomena to the nonlinear generalized Hietarinta-type equation

Abstract

In this paper, we describe the nonlinear behavior of a generalized fourth-order Hietarinta-type equation for dispersive waves in (2 + 1) dimension. The various wave formations are retrieved by using Hirota’s bilinear method (HBM) and various test function perspectives. The Hirota method is a widely used and robust mathematical tool for finding soliton solutions of nonlinear partial differential equations (NLPDEs) in a variety of disciplines like mathematical physics, nonlinear dynamics, oceanography, engineering sciences, and others requires bilinearization of nonlinear PDEs. The different wave structures in the forms of new breather, lump-periodic, rogue waves, and two-wave solutions are recovered. In addition, the physical behavior of the acquired solutions is illustrated in three-dimensional, two-dimensional, density, and contour profiles by the assistance of suitable parameters. Based on the obtained results, we can assert that the employed methodology is straightforward, dynamic, highly efficient, and will serve as a valuable tool for discussing complex issues in a diversity of domains specifically ocean and coastal engineering. We have also made an important first step in understanding the structure and physical behavior of complex structures with our findings here. We believe this research is timely and relevant to a wide range of engineering modelers. The results obtained are useful for comprehending the fundamental scenarios of nonlinear sciences.