Frequency shifting for solitons based on transformations in the Fourier domain and applications.

• The theoretical procedures for shifting the frequency of solitons are proposed. • These procedures are confirmed by numerical simulations with the propagation model. • Stabilizing soliton propagation and controlling soliton collisions are presented. • The results open a way for controlling soliton frequency and soliton dynamics. We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schrödinger equation. The procedures are based on simple transformations of the soliton pattern in the Fourier domain and on the shape-preserving property of solitons. These theoretical frequency shifting procedures are verified by numerical simulations with the nonlinear Schrödinger equation using the split-step Fourier method. In order to demonstrate the use of the frequency shifting procedures, two important applications are presented: (1) stabilization of the propagation of solitons in waveguides with frequency dependent linear gain-loss; (2) induction of repeated soliton collisions in waveguides with weak cubic loss. The results of numerical simulations with the nonlinear Schrödinger model are in very good agreement with the theoretical predictions. [ABSTRACT FROM AUTHOR]