Breather and its interaction with rogue wave of the coupled modified nonlinear Schrödinger equation

Abstract In this paper, we investigate the coupled modified nonlinear Schrödinger equation. Breather solutions are constructed through the traditional Darboux transformation with the nonzero plane-wave solutions. To obtain the higher-order localized wave solution, N -fold generalized Darboux transformation is given. Under the condition that the characteristic equation admits a double-root, we present the expression of first-order interactional solution. Then we graphically analyze the dynamics of breather and rogue wave. Due to the simultaneous existence of nonlinear and self-steepening terms in the equation, there presents different profile in two components for the breathers.