Autophasing of solitons

Resonant control of solitons

“…For the closed trajectories, the associated phase difference varies only in the finite range δ − δ 0 (τ ) δ + , thus, the phase of the soliton is captured by the driving. In this case one can control soliton parameters by varying the driving frequency (autoresonant control) [7,9]. Obviously, the capture occurs only when the phase point at the initial time gets into a small domain of the phase space located inside the separatrix loop.…”

“…It imposes a strong restrictions on the initial parameters of the soliton. It needs to know the amplitude of the soliton with accuracy ∼ √ ε to determine correctly the resonant frequency and, in addition, some complex conditions for synchronization of phases of the soliton and the driving should be applied [7]. Both conditions are difficult to satisfy and the capture of a soliton by the driving seems rather exclusive effect in typical experimental conditions.…”

“…[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.…”

“…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. However, the method appears very difficult for applications because the capture of the soliton of a finite amplitude occurs only in a narrow range of the driving frequencies and with strong restrictions on the phase of the driving [7]. In this Letter we propose that, in contrast to the autoresonance, the promising method of control and amplification of solitons can be based on the "scattering on resonance" [9][10][11] without capture of the soliton.…”

Control of solitons

“…A specific problem is the autoresonant control of already existing high amplitude solitons. For the one-phase driving, this problem has been studied for the sine-Gordon [19] and NLS equations [20]. * shagalov@imp.uran.ru…”