Rogue waves and solitons of the coherently-coupled nonlinear Schrödinger equations with the positive coherent coupling

A set of the coherently-coupled nonlinear Schrödinger equations with the positive coherent coupling terms, which are related to the optical fiber communication, are studied through the binary Darboux transformation with the dimensional reduction. Formalisms of the solutions appear as the mixtures of the polynomial functions with exponential functions. When the spectral parameter is real, we obtain different kinds of the solutions, such as the soliton, degenerate-soliton, periodic, and soliton-like rational solutions. When the spectral parameter is complex with a non-zero imaginary part, we obtain the rogue waves and twisted rogue-wave pairs, and show that an eye-shaped rogue wave splits into a twisted rogue-wave pair.