  We show that the breaking of integrability in the fundamental one-dimensional
model of bosons with contact interactions has consequences on the stationary
correlation properties of the system. We calculate the energies and correlation
functions of the integrable Lieb-Liniger case, comparing the exact Bethe-ansatz
solution with a corresponding Jastrow ansatz. Then we examine the
non-integrable case of different interaction strengths between each pair of
atoms by means of a variationally optimized Jastrow ansatz, proposed in analogy
to the Laughlin ansatz. We show that properties of the integrable state are
more stable close to the Tonks-Girardeau regime than for weak interactions. All
energies and correlation functions are given in terms of explicit analytical
expressions enabled by the Jastrow ansatz. We finally compare the correlations
of the integrable and non-integrable cases and show that apart from symmetry
breaking the behavior changes dramatically, with additional and more pronounced
maxima and minima interference peaks appearing.
