  We analyze the macroscopic dynamics of a Bose gas in a harmonic trap with a
superimposed two-dimensional optical lattice, assuming a weak coupling between
different lattice sites. We consider the situation in which the local chemical
potential at each lattice site can be considered as that provided by the
Lieb-Liniger solution. Due to the weak coupling between sites and the form of
the chemical potential, the three-dimensional ground-state density profile and
the excitation spectrum acquire remarkable properties different from both 1D
and 3D gases. We call this system a quasi-Tonks gas. We discuss the range of
applicability of this regime, as well as realistic experimental situations
where it can be observed.
