Higher-order rational and semi-rational rogue wave solutions in the coupled complex mKdV equations

In this talk, we mainly investigate the dynamics of the localized solutions for the coupled complex mKdV equations  with a detailed process. Firstly, based on the Lax pair, the generalized Darboux transformation is presented. Based on modulation instability, two types of nth order rational rogue wave solutions in compact determinant forms have been derived. In the second part,the Darboux-dressing transformation of the equation is also presented. With the aid of an asymptotic expansion theory, we derive the concrete forms of the higher-order interactional localized solutions. The dynamic behaviors of localized solutions are elucidated from the viewpoint of three-dimensional structures. These results further uncover some striking dynamic structures in multi-component coupled system.