Qualitative interaction dynamics of lump-type and breather structures in coupled Boussinesq system

Abstract We investigate the qualitative interaction dynamics of localized nonlinear wave structures in the coupled Boussinesq (CB) system using the Hirota bilinear method (HBM). Lump-type analytical wave profiles are constructed using a positive quadratic polynomial within Hirota’s perturbative framework, and their localized behavior is primarily examined through graphical analysis. The interactions between lump-type structures and one or two-kink waves are explored, revealing the formation of double lump-type structures near the central space–time region. In addition, breather structures are analyzed, exhibiting diffusion-like and interaction behaviors under suitable parameter regimes. The interaction of breather structures with periodic waves, kink waves, and bright soliton profiles is demonstrated, along with interaction scenarios involving two chains of double breathers. All results are illustrated through detailed two-dimensional, three-dimensional, and contour plots, highlighting the dominant localized dynamics near the center of the ( x , t )-plane. This study provides a qualitative understanding of lump-type and breather interaction phenomena in the CB system, highlighting its rich nonlinear wave dynamics.