  An integrable model subjected to a periodic driving gives rise generally to a
non-integrable Floquet Hamiltonian. Here we show that the Floquet Hamiltonian
of the integrable Lieb--Liniger model in presence of a linear potential with a
periodic time--dependent strength is instead integrable and its quasi-energies
can be determined using the Bethe ansatz approach. We discuss various aspects
of the dynamics of the system at stroboscopic times and we also propose a
possible experimental realisation of the periodically driven tilting in terms
of a shaken rotated ring potential.
