Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions

We consider the dynamics of dark matter wave solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic-quintic nonlinearity modelling two- and three-body interactions, respectively. Opposite to the usual (cubic) Gross-Pitaevskii equation for which the dark soliton effective mass is known to be constant (equal to 2), in the presence of a cubic-quintic nonlinearity we find that the effective mass depends on the product of the initial density background and the ratio between the coefficient of quintic and cubic nonlinearities, this leading to the interesting possibility of measuring three-body interactions directly from the dark soliton dynamics. A comparison between analytical results and direct numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good agreement between them which confirms the validity of our approach.