  One-dimensional Bose gases are considered, interacting either through the
hard-core potentials or through the contact delta potentials. Interest in these
gases gained momentum because of the recent experimental realization of
quasi-one-dimensional Bose gases in traps with tightly confined radial motion,
achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For
such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of
the present communication is to give a brief survey of the problem and to
demonstrate the generality of this mapping by emphasizing that: (i) It is valid
for nonequilibrium wavefunctions, described by the time-dependent Schr\"odinger
equation, not merely for stationary wavefunctions. (ii) It gives the whole
spectrum of all excited states, not merely the ground state. (iii) It applies
to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas
of impenetrable bosons.
