Multi-lump, lump-kink and interaction of breather with other nonlinear waves of a couple Boussinesq system

We investigate the interaction characteristics of nonlinear coherent structures in the couple Boussinesq (CB) system using the Hirota bilinear approach. First, we derive the lump solutions using a positive quadratic polynomial within the Hirota perturbation technique. Next, We study the explicit interactions between lumps and one or two-kink waves, and observe double lump patterns. Furthermore, we discover the interactions of breathers, revealing a diffusion-like behavior. We notice that breather waves can interact with periodic, kink, and bright solitons for specific parameter sets in the CB system. Interactions between two chains of double breathers are also found. We analyze our results using a combination of symbolic computations and graphical representations, providing a deeper understanding of their behavior. This study reveals previously unreported nonlinear dynamics in the CB system.