N-soliton solutions and nonlinear dynamics for two generalized Broer–Kaup systems

• Published in: Nonlinear dynamics Vol. 107; no. 1; pp. 1179 - 1193
• Main Authors: Zhang, Sheng, Zheng, Xiaowei
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2022; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Dynamical Systems; Engineering; Mechanical Engineering; Nonlinear dynamics; Original Paper; Solitary waves; Vibration; Hirota’s bilinear method; Nonlinear dynamics; soliton solution; Bilinear form; gBK equations
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-07030-w

Under consideration in this paper are two nonlinear evolution models: One is the (1 + 1)-dimensional generalized Broer–Kaup (gBK) system derived by Zhang et al. (Appl Math Comput 219:5837–5848, 2013), and the other is the (2 + 1)-dimensional gBK system reported for the first time. Based on the bilinear forms given in this paper, novel N -soliton solutions of these two gBK systems are obtained by using Hirota’s bilinear method. As a comparison, the obtained two-soliton solutions of the (1 + 1)-dimensional gBK system are taken to demonstrate the difference from the known ones constructed by Darboux transformation. In order to understand the nonlinear dynamics localized in the gBK systems, local structures of the obtained one-, two-, three- and four-soliton solutions are shown. This paper reveals that each pair of the obtained N -soliton solutions of the gBK systems couple bell and kink soliton dynamics.