Diverse interference of nonlinear waves on the non-zero background in the coherently coupled system

Diverse interference phenomena of various nonlinear waves on the non-zero background in the weakly birefringent fiber are explored based on a generic linear transformation with multiple free parameters. By selecting appropriate parameters, the vectors in the transformation can be modulated, and the controllable interference phenomena can be achieved. It is found that the free parameters affect the pulse profile of the interference waves between single dark-solitons, pulse width of the interference waves between double dark-solitons, and the interference pattern of the breathers, while the parameters of dark-soliton/breather mainly influence the background of the interference waves. Abundant interference phenomena of other nonlinear waves can be investigated by using the derived generic linear transformation, and the results presented here may be useful for constructing multi-speed solitons and designing diverse interference patterns for optical printing.