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Updated: Apr 17, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
Autoresonant excitation of dark solitons
M A Borich1, A G Shagalov1, L Friedland2
1Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation.
Abstract:
Continuouslyphase-locked (autoresonant) dark solitons of the defocusing nonlinear Schrodinger equation are excited and controlled by driving the system by a slowly chirped wavelike perturbation. The theory of these excitations is developed using Whitham's averaged variational principle and compared with numerical simulations. The problem of the threshold for transition to autoresonance in the driven system is studied in detail, focusing on the regime when the weakly nonlinear frequency shift in the problem differs from the typical quadratic dependence on the wave amplitude. The numerical simulations in this regime show a deviation of the autoresonance threshold on the driving amplitude from the usual 3/4 power dependence on the driving frequency chirp rate. The theory of this effect is suggested.
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