Dynamic behaviors of the interaction solutions of the Zakharov equation

This paper aims to employ the Darboux transformation (DT) to discover the interaction solutions of the Zakharov equation (Eq. (1.2) for delta=1). Through partial degradation of eigenvalues, interaction solutions of the model are constructed on the basis of high-order breather solutions. The study derives interaction solutions involving breather and b-positon solutions through partial degradation of eigenvalues (lambda j ->lambda 1). Further, interaction solutions comprising breather and lump solutions are obtained through partial double degradation of eigenvalues (lambda j ->lambda 0). Then, several interaction solutions containing b-positon and lump solutions are extracted through mixed degradation of eigenvalues (lambda j ->lambda 1 and lambda k ->lambda 0). In particular, the dynamic evolution characteristics of these solutions are studied. It is believed that these studies make a significant contribution to the understanding of the Zakharov equation and its possible applications in physics.