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The collective oscillations of 1D repulsive Bose gas with external harmonicconfinement in two different regimes are studied. The first regime is the meanfield regime when the density is high. The second regime is the Tonks-Girardeauregime when the density is low. We investigate the resonances under periodicmodulations of the trap potential and the effective nonlinearity. Modulationsof the effective nonlinear coefficient result from modulations of the atomicscattering length by the Feshbach resonance method or variations of thetransverse trap frequency. In the mean field regime we predict the bistabilityin the nonlinear oscillations of the condensate. In the Tonks-Girardeau regimethe resonance has the character of a linear parametric resonance. In the caseof rapid strong modulations of the nonlinear coefficient we find analyticalexpressions for the nonlinearity managed soliton width and the frequency of theslow secondary oscillations near the fixed point.Comment: 16 pages, 7 figure

Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length