High-order semi-rational solutions for the coherently coupled nonlinear Schrödinger equations with the positive coherent coupling

A coherently coupled nonlinear Schrödinger system with the positive coherent coupling is studied in this paper, and high-order semi-rational solutions are derived by the generalized Darboux transformation. Dynamic of the second-order semi-rational solutions is found to be of three types: collisions between the one-hump soliton and breather (double-hump rogue waves), collisions between the double-hump soliton and breather (double-hump rogue waves), and bound states of the one-hump solitons or double-hump solitons. Furthermore, for the third-order semi-rational solutions, three double-hump solitons and three one-hump solitons are found to be attracted and repulsed with each other periodically.