Abstract
We investigate the variable-coefficient generalized higher order nonlinear Schrödinger equation which governing the attosecond optical soliton propagation in an inhomogeneous fiber system. Three-soliton solutions are attained through Darboux transformation based on the Lax pair. Using three soliton solutions, we investigate the periodic and nonperiodic amplification of three solitons by adopting certain functions to variable coefficients. Various amplification schemes are demonstrated graphically via symbolic computation. Especially, periodic and nonperiodic amplifications are attained under dispersion and nonlinearity management. In order to realize the soliton amplifications, two different set of variable coefficients profiles are employed. The results obtained in this work will be helpful for designing the optical amplification devices by soliton control technology.