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 Schrödinger
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.