Interactions of breathers and rogue wave for the coupled Lakshmanan–Porsezian–Daniel equation

Interactions of nonlinear waves play a significant role in physical systems. In this work, we attain the interactions of breathers and rogue wave for the coupled Lakshmanan–Porsezian–Daniel equation. Through the Darboux transformation, we succeed the interactional solutions consisting of different types of breathers and rogue wave. In particular, it can be observed that distinct parameters \(a_1\) $a_1$ , \(a_2\) $a_2$ , \(\delta \) $\delta$ and \(\lambda _1\) ${\lambda }_1$ make the interaction properties, structures and energy conversion of breathers and dramatically change. Moreover, we exhibit the striking dynamics of interactional solutions based on three-dimensional figures. These results are helpful for the study of nonlinear waves in coupled integrable systems.