  We determine the ground-state energy and the effective dispersion law for a
one-dimensional system of point bosons under zero boundary conditions. The
ground-state energy is close to the value for a periodic system. But the
dispersion law is essentially different from that for a periodic system, if the
coupling is weak (weak interaction or high concentration) or intermediate. We
propose also a new method for construction of the thermodynamics for a gas of
point bosons. It turns out that the difference in the dispersion laws of
systems with periodic and zero boundary conditions does not lead to a
difference in the thermodynamic quantities. In addition, under zero boundary
conditions, the microscopic sound velocity does not coincide with the
macroscopic one. This means that either the method of determination of $k$ in
the dispersion law $E(k)$ is unsuitable or the low-energy excitations are not
phonons.
