Vibration spectrum of a two-soliton molecule in dipolar Bose–Einstein condensates

We study the vibration of soliton molecules in dipolar Bose–Einstein condensates by variational approach and numerical simulations of the nonlocal Gross–Pitaevskii equation. We employ the periodic variation of the strength of dipolar atomic interactions to excite oscillations of solitons near their equilibrium positions. When the parametric perturbation is sufficiently strong the molecule breaks up into individual solitons, like the dissociation of ordinary molecules. The waveform of the molecule and resonance frequency, predicted by the developed model, are confirmed by numerical simulations of the governing equation.