Breather waves, high-order rogue waves and their dynamics in the coupled nonlinear Schr?dinger equations with alternate signs of nonlinearities

摘要： We consider the analytic vector breather and high-order rogue wave solutions for the coupled nonlinear Schr?dinger (NLS) equations with alternate signs of nonlinearities via Darboux dressing transformation. By adjusting spectral parameters, we indicate that the breather wave solutions contain temporally periodic nonlinear waves and spatially periodic nonlinear waves, respectively. The vector rogue wave solutions include the bright one-peak-two-valleys rogue wave and the bright rogue wave without valleys. Additionally, we successfully show different types of the distributions for the second-order vector rogue waves. The existence condition for the rogue waves is discussed. For the coupled NLS equations with alternate signs of nonlinearities, the rogue wave solutions exist if the baseband modulation instability (MI) is present.