Soliton solutions via auxiliary function method for a coherently-coupled model in the optical fiber communications

A coherently-coupled nonlinear Schrödinger system in the optical fiber communications, with the mixed self-phase modulation (SPM), cross-phase modulation (XPM) and positive coherent coupling terms, is studied through the bilinear method with an auxiliary function. Solutions for that system are found to be of two types: singular and non-singular ones, and the latter appear as the soliton-typed. Vector bright one- and two-solitons are derived with the corresponding phase-shift parameter constraints. In virtue of computerized symbolic computation and asymptotic behavior analysis, elastic collision mechanisms of such vector solitons are investigated. With the aid of graphical simulation, vector solitons are displayed to be of the single- or double-hump profiles. The formation and collision mechanisms of the vector bright solitons for that system are generated based on the combined effects of SPM, XPM and coherent coupling. Only elastic collisions of the vector solitons occur for that system, which is a distinctive feature amid those of other coherently-coupled nonlinear Schrödinger systems.