Control of solitons

Abstract

A method for adiabatic control of envelope solitons in the driven nonlinear Schrödinger equation is developed. The approach is based on the autoresonant effect, when the soliton is captured ("phase locked") by a two-phase resonant driving with slowly varying frequencies. Threshold conditions for amplitudes and variation rates of the driving required for the control of both the amplitude and the velocity of the soliton are found. Numerical simulations demonstrate that the method allows one to control solitons for a long time according to a given scenario, while the threshold conditions are fulfilled locally.

Feedback control for some solutions of the sine-Gordon equation

“…Previously these methods were mainly used for oscillation control problems for systems governed by ordinary differential equations [9,12]. Use of the control mechanism in the wave processes concern envelope wave equations [7,13], reaction-diffusion equations [14,15], and the sine-Gordon equation [8,16,17]. Some control related methods for sin-Gordon equation use feedforward (nonfeedback) controlling actions [7,13].…”

“…Use of the control mechanism in the wave processes concern envelope wave equations [7,13], reaction-diffusion equations [14,15], and the sine-Gordon equation [8,16,17]. Some control related methods for sin-Gordon equation use feedforward (nonfeedback) controlling actions [7,13]. The other ones apply control changing the equation completely, and do not using measurement of the current system state [14,15].…”

Switching dynamics and linear response spectra of a driven one-dimensional nonlinear lattice containing an intrinsic localized mode

“…Given sufficient starting amplitude it will stay in resonance as the driving frequency is changed adiabatically. In the resultant autoresonant (AR) state the driver frequency controls the ILM amplitude [30][31][32][33][34][35]. This AR-ILM is stable * msato@kenroku.kanazawa-u.ac.jp between two bifurcation frequencies when the driver frequency is the control parameter [22,26].…”

Resonant control of solitons

“…[6][7][8]. The method was based on the autoresonant phenomenon when the soliton was captured by the resonant driving with the frequency close to the internal frequency of the soliton.…”