Multihump bright–dark solitons in the multicomponent Mel’nikov system

As an important type of nonlinear localized structure, multihump solitons have attracted considerable attention in various physical fields, such as nonlinear optics, Bose–Einstein condensates, and fluid dynamics. Motivated by this background, this paper presents an in-depth investigation of multihump solitons in the multicomponent Mel’nikov system. Firstly, based on the KP hierarchy reduction method combined with the construction condition of multihump solitons, multihump bright–dark soliton solutions of the system are derived. Secondly, the structural stability of multihump solitons is analyzed in detail, and the effects of relevant parameters on waveform characteristics, such as the hump spacing, symmetry, and grayness, are further examined. Finally, by means of asymptotic analysis, the interaction dynamics among double-hump solitons, as well as between double-hump solitons and degenerate single-hump solitons, are explored, thereby revealing the distinct dynamical characteristics of these two types of interactions.