Diverse composite waves in coherently coupled inhomogeneous fiber systems with external potentials

In this paper, we focus on the coherently coupled nonlinear Schrodinger (NLS) equations with variable coefficient including four-wave mixing, external potential and gain/loss terms, and derive three types of similarity transformations under different constraint conditions. Based on these transformations, one can transform the variable coefficient coupled NLS equations into constant coefficient coupled NLS equations that can be decoupled by using of a linear transformation. Thus, various composite waves superposed by different nonlinear waves can be investigated in homogeneous and inhomogeneous systems with the aid of the solutions of NLS equation and these transformations. The diversity of various composite waves and the energy exchange between two coherently coupled components in homogeneous fiber system are demonstrated. Furthermore, based on the obtained three types of similarity transformations, the characteristics of the composite waves are investigated in tunneling system and periodic perturbation system, respectively. These results could be helpful to explore the diverse dynamics of the composite waves in birefringent fiber.