Multiple rogue waves solutions for a (3 + 1)-dimensional nonlinear wave in liquid with gas bubbles via Hirota bilinear equation method

In this study, we employ a symbolic computation approach to construct various rogue wave solutions of the (3+1)-dimensional nonlinear wave equation modeling wave propagation in a liquid medium containing gas bubbles. Through the application of the Hirota bilinear method, we systematically derive first-order, second-order, and third-order rogue wave solutions. By selecting appropriate parameter values, we generate graphical illustrations that reveal the structural features and interaction dynamics of these rogue waves. A variety of soliton solutions were obtained from the analysis. Upon plotting these solutions, several rogue wave solutions emerged and periodic waveforms. These results are visually represented through two-dimensional, three-dimensional, and contour plots to highlight the different features and behaviors of each solution. The analysis enhances our understanding of rogue wave behavior within the context of the modeled physical system.