Localized waves solutions for the fifth-order coupled extended modified KdV equation

The fifth-order coupled extended modified Korteweg-de-Vries (KdV) equation is studied. Based on seed solutions and Lax pairs, the Nth-order iterative expression of the localized wave solutions of the equation are obtained by the generalized Darboux transformation. Then, through numerical simulation, the evolution plots of the interaction of rogue waves with dark-bright solitons and the Kuznetsov-Ma breathers are derived. The results demonstrate the abundant dynamical patterns of localized waves in the fifth-order coupled systems.