Interaction of solitons in elongated BEC with time-dependent trap

The interaction of matter-wave solitons in elongated Bose–Einstein condensate with time-dependent parabolic trap is investigated using the perturbation theory based on the inverse scattering transform. Regimes of parametric and main resonances in solitons interactions are investigated for harmonic trap potentials. The predictions of the theory are confirmed by the numerical simulations of the quasi-one-dimensional Gross–Pitaevskii equation.