Dynamical analysis of higher-order localized waves for a three-component coupled nonlinear Schrödinger equation

Abstract This paper examines the three-component coupled nonlinear Schrödinger equation, which has various applications in deep ocean, nonlinear optics, Bose–Einstein (BE) condensates, and more. On the basis of seed solutions and a Lax pair, the N th-order iterative expressions for the solutions are derived by using the generalized Darboux transformation. The evolution plots of dark-bright-rogue wave or breather-rogue wave are then obtained via numerical simulation. Particularly, a novel rogue wave propagation trajectory is found in the second and third order localized wave solutions. Moreover, by increasing the value of the free parameter α and β , the nonlinear waves merge with each other distinctly. The results further reveal the abundant dynamical patterns of localized waves in the three-component coupled system.