We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for
the Lieb-Liniger model in a linear (constant force) potential (the constructed
exact stationary solutions are referred to as the Lieb-Liniger-Airy wave
functions). The ground state properties of the gas in the wedge-like trapping
potential are calculated in the strongly interacting regime by using
Girardeau's Fermi-Bose mapping and the pseudopotential approach in the
1/c-approximation (c denotes the strength of the interaction). We point out
that quantum dynamics of Lieb-Liniger wave packets in the linear potential can
be calculated by employing an N-dimensional Fourier transform as in the case
of free expansion
