Symbolic computation on soliton solutions for variable-coefficient nonlinear Schrödinger equation in nonlinear optics

Soliton interaction and control using the dispersion-decreasing fibers with potential applications to the design of high-speed optical devices and ultralarge capacity transmission systems are investigated based on solving the variable-coefficient nonlinear Schrödinger equation with symbolic computation. Via the Hirota method, analytic two- and three-soliton solutions for that model are obtained, with their relevant properties and features illustrated. Dispersion-decreasing fibers with different profiles are found to be able to control the soliton velocity. Additionally, through the asymptotic analysis for the two-soliton solutions, we point out that the interaction between two solitons is elastic. Finally, a new approach to controll the soliton interaction using the dispersion-decreasing fiber with the Gaussian profile is suggested.