  We derive the exact solution of low energy limit of Bogoliubov equations for
excitations of Bose-Einstein condensate in the presence of arbitrary potential
barrier and maximum current of condensate. Using this solution, we give the
explicit expression for the transmission coefficient against the potential
barrier, which shows partial transmission in the low energy limit. The
wavefunctions of excitations in the low energy limit do not coincide with that
of the condensate. The absence of the perfect transmission in the critical
current state originates from local enhancement of density fluctuations around
the potential barrier.
