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The dynamics of a two-soliton molecule bouncing on the reflecting atomicmirror under the effect of gravity has been studied by analytical and numericalmethods. The analytical description is based on the variational approximation.In numerical simulations, we observe the resonance oscillations of thetwo-soliton's center-of-mass position and width, induced by modulated atomicmirror. Theoretical predictions are verified by numerical simulations of thenonlocal Gross-Pitaevskii equation (GPE) and qualitative agreement between themis found. Hamiltonian dynamic system for a dipolar Bose-Einstein condensates(BECs) has been studied.

Two-soliton molecule bouncing in a dipolar Bose-Einstein condensates under the effect of gravity