Looking at a nonlinear inhomogeneous optical fiber through the generalized higher-order variable-coefficient Hirota equation

Optical fiber communication system is one of the core supporting systems of the modern internet age, and studies on the ultrashort optical pulses are at the forefront of fiber optics, modern optics and optical engineering. Hereby, symbolic computation on the recently-proposed generalized higher-order variable-coefficient Hirota equation is performed, for certain ultrashort optical pulses propagating in a nonlinear inhomogeneous fiber. For the complex envelope function associated with the optical-pulse electric field in the fiber, an auto-Bäcklund transformation is worked out, along with a family of the analytic solutions. Both our Bäcklund transformation and analytic solutions depend on the optical-fiber variable coefficients which represent the effects of the first-order dispersion, second-order dispersion, third-order dispersion, Kerr nonlinearity, time delaying, phase modulation and gain/loss. Relevant constraints among those coefficients are also presented. We expect that the work could be of some use for the fiber-optics investigations.