Periodic solitons and their interactions for a general coupled nonlinear Schrödinger system

Studied in this paper is a general two-coupled nonlinear Schrödinger system, in which the coefficients of the self-phase modulation, cross-phase modulation and four-wave mixing terms are arbitrary. With the Hirota method, the bilinear form and periodic one- and two-soliton solutions are derived. Propagation characteristics of periodic solitons are mainly discussed. Under certain conditions, not only general mixed-type vector soliton solutions can be gotten from our results such as bright-dark, dark-bright and bright-bright solitons, but also some new mixed-type vector soliton solutions are generated, including bright-periodic, periodic-bright, dark-periodic and periodic-dark solitons. Dynamic behaviors of those solitons are discussed through graphic simulation.