Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters P_{1,2,3} are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the P_{1,2,3} parameter space, the system may exhibit two very different evolutions, i.e., the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analyzed both in theory and simulations with the emphasis on the effect of the interaction parameter P_{3}. In particular, the transition thresholds on the driving parameter P_{1} and their width in P_{1} in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and deexcitation of the condensate.

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.

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It is shown that the effect of "scattering on resonance" can be used to control envelope solitons in the driven nonlinear Schrödinger equation. The control occurs by the frequency modulated driving with multiple crossing of the resonant frequency of the soliton.Crown

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