Abstract

We report exotic hybrid rogue wave and breather solutions for a complex mKdV equation describing soliton dynamics in shallow water wave and optics. Starting from the Lax pair, the higher-order Darboux transformations for the equation are constructed. Further, we obtain a series of theorems to compute the hybrid rogue wave and breather solutions. We also demonstrate the interaction features between rogue waves and breathers by controlling parameters. These results are of importance to understand nonlinear wave dynamics in water wave systems.