Hamiltonian of the N-boson system can be time-dependent:

External, generally time-dependent trapping potential, trap is used to confine bosons (ultra-cold atoms).

Inter-boson interaction, can be time-dependent, very often it is approximated by a dirac-delta function (contact interaction)

Strength of the interaction, if it is positive the interaction is repulsive, if it is negative -- it is attractive, i.e., bosons attract each other.

We use the MCTDHB method to solve the TDSE.

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MCTDHB  is the acronym of  Multi-Configurational Time-Dependent Hartree for Bosons