Rogue Waves and Their Dynamics on Bright-Dark Soliton Background of the Coupled Higher Order Nonlinear Schrodinger Equation

The coupled higher order nonlinear Schrodinger equation is investigated by using the Darboux-dressing transformation with the Lax pair and asymptotic expansion method. Based on the Lax pair, we first construct the generalized Darboux transformation of the equation. Then, we construct the first-order breather wave solution expressed in terms of hyperbolic function and exponential function. Moreover, using a taylor expansion method, we naturally obtain the first, second, third even higher order rogue wave solutions. Actually, when one of a(1), a(2) equates to zero, the corresponding breather wave and rogue wave will propagate along with multiple bright-dark soliton background, which are also respectively called the superposition of breather wave and rogue wave with multiple bright-dark solitons. By applying a variable separation transformation with the third-order constant vector w, the higher-order rogue wave will transfer to the multiple independent rogue waves and present a triangular. These nonlinear phenomena can be used to understand the dynamics of the rogue wave propagation on some important nonlinear medias. Our results show that the multi-component nonlinear systems also contain the more interesting nonlinear dynamics than other single-component systems.