title: 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.
authors.affiliation: Institute of Metal Physics, Ekaterinburg, Russian Federation.
authors.forename: S V
authors.initials: SV
authors.lastname: Batalov
authors.forename: A G
authors.initials: AG
authors.lastname: Shagalov