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Frequency shifting for solitons based on transformations in the Fourier domain and applications. (English) Zbl 1481.35357

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Software:

Matlab
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References:

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