  We analyze stationary current of bosonic carriers in the Bose-Hubbard chain
of length $L$ where the first and the last sites of the chain are attached to
reservoirs of Bose particles acting as the particle source and sink,
respectively. The analysis is curried out by using the pseudoclassical approach
which reduces the original quantum problem to the classical problem for $L$
coupled nonlinear oscillators. It is shown that an increase of oscillator
nonlinearity (which is determined by the strength of inter-particle
interactions) results in a transition from the ballistic transport regime,
where the stationary current is independent of the chain length, to the
diffusive regime, where the current is inverse proportional to $L$.
