Hybrid structures of localized waves for the coupled extended mKdV equation

Abstract

For the coupled extended modified Korteweg–de Vries (mKdV) equation, we investigate hybrid structure waves composed of localized waves. This equation can be considered as the generalization of the mKdV equation. Firstly, hybrid structures of localized waves can be derived in view of the generalized Darboux transformation. Next, we get different interactions between those hybrid waves with the parameters changing. After that, it is found that under a certain condition, the hybrid solutions will degenerate into rational solutions. In particular, we find an interesting rational rogue wave with the novel dynamical behavior. In addition, we show the striking dynamics of hybrid solutions by analyzing each figure. These new solutions can help us investigate integrable systems better.