On a variable-coefficient AB system in a baroclinic flow: Generalized Darboux transformation and non-autonomous localized waves

• Published in: Wave motion 2023-10, Vol.122, p.103184, Article 103184
• Main Authors: Wu, Xi-Hu, Gao, Yi-Tian, Yu, Xin, Liu, Fei-Yan
• Format: Article
• Language: English
• Subjects: Baroclinic flow; Bound state; Generalized Darboux transformation; Non-autonomous localized wave; symbolic computation; Variable-coefficient AB system
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2023.103184

In this paper, we focus our attention on a variable-coefficient AB system, which models the marginally unstable baroclinic wave packets in a baroclinic flow. With respect to the amplitude of the baroclinic wave packet and correction to the mean flow resulting from the self-rectification of the baroclinic wave, we construct an N-fold generalized Darboux transformation (GDT) via symbolic computation, where N is a positive integer. Via the obtained GDT, several kinds of the non-autonomous localized waves, e.g., the multi-pole solitons, multi-pole breathers, rogue waves and their interactions, are investigated. We have selected four types of the variable coefficients, i.e., constant, linear about t, quadratic about t and trigonometric about t, where t is the normalized retarded time coordinate. We explore the influence of those selected variable coefficients on the non-autonomous localized waves. Moreover, we discuss the bound states among the non-autonomous multiple-pole solitons and one soliton, which exhibit the periodic attractions and repulsions between the adjacent solitons. •We construct an N-fold generalized Darboux transformation for a variable-coefficient AB system in a baroclinicflow.•Several kinds of the non-autonomous localized waves and their bound-states are investigated.•Effects of the variable coefficients on the above non-autonomous localized waves are explored.