M-lump, rogue waves, breather waves, and interaction solutions among four nonlinear waves to new (3+1)-dimensional Hirota bilinear equation

• Published in: Nonlinear dynamics Vol. 111; no. 10; pp. 9477 - 9494
• Main Authors: Wang, Binji, Ma, Zhimin, Xiong, Sihan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2023; Springer Nature B.V
• Subjects: Acoustic waves; Algebra; Automotive Engineering; Breathers; Classical Mechanics; Control; Dynamical Systems; Engineering; Fluid mechanics; Mechanical Engineering; Nonlinear phenomena; Original Paper; Parameters; Physics; Plasma physics; Propagation; Propagation velocity; Shallow water; Solitary waves; Vibration; Wave propagation; Long-wave limit method; Dynamical behavior; Higher-order breather; Interaction solutions; Hirota bilinear method
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08338-5

In this research article, we study a new (3+1)-dimensional Hirota bilinear equation which can describe the dynamics of ion-acoustic wave and Alvin wave of small but finite amplitude in plasma physics and describe the propagation process of nonlinear waves in shallow water. First, we apply two methods to study the equation, namely the Hirota bilinear method and long-wave limit method M-lump solution, and line rogue waves are reported. Furthermore, we investigate the velocity, propagation trajectory, and interaction phenomenon of M-lump solution(M=2,3). Then, based on the multi-solitons, two cases of high-order breather solution are constructed by selecting some special parameters. Finally, four types interaction solutions are successfully obtained by employing long-wave limit method and selecting some special parameters. More importantly, we explore physical collision phenomenon of the interaction between nonlinear waves. In order to better illustrate the characteristics of the interaction solutions, the results are shown in three-dimensional plots and numerical simulation. To our knowledge, all of the obtained solutions in this article are novel. The results of this article may be provide an important theoretical basis for explaining some nonlinear phenomena in the field of fluid mechanics and shallow water.