Symbolic-computation study of the perturbed nonlinear Schrödinger model in inhomogeneous optical fibers

A realistic, inhomogeneous fiber in the optical communication systems can be described by the perturbed nonlinear Schrödinger model (also named as the normalized nonlinear Schrödinger model with periodically varying coefficients, dispersion managed nonlinear Schrödinger model or nonlinear Schrödinger model with variable coefficients). Hereby, we extend to this model a direct method, perform symbolic computation and obtain two families of the exact, analytic bright-solitonic solutions, with or without the chirp respectively. The parameters addressed include the shape of the bright soliton, soliton amplitude, inverse width of the soliton, chirp, frequency, center of the soliton and center of the phase of the soliton. Of optical and physical interests, we discuss some previously-published special cases of our solutions. Those solutions could help the future studies on the optical communication systems.