Dynamic behaviors of the interaction solutions of the Zakharov equation

Abstract

This paper aims to employ the Darboux transformation (DT) to discover the interaction solutions of the Zakharov equation (Eq. ( 1.2 ) for [Formula: see text]). 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 ([Formula: see text]). Further, interaction solutions comprising breather and lump solutions are obtained through partial double degradation of eigenvalues ([Formula: see text]). Then, several interaction solutions containing b-positon and lump solutions are extracted through mixed degradation of eigenvalues ([Formula: see text] and [Formula: see text]). 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.