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

• Published in: Examples and counterexamples Vol. 8; p. 100202
• Main Authors: Awad, Mohamed M., Elsadany, A.A., Elboree, Mohammed K.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2025; Elsevier
• Subjects: (3 + 1)-dimensional nonlinear wave in liquid with gas bubbles; Bilinear form; Rogue waves; Symbolic computation approach; Rogue waves; Symbolic computation approach; Bilinear form; (3 + 1)-dimensional nonlinear wave in liquid with gas bubbles
• ISSN: 2666-657X; 2666-657X
• DOI: 10.1016/j.exco.2025.100202

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.