  In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons
interacting by a repulsive \delta-potential and calculated the ground state in
the thermodynamic limit. In the present work, we extend this model to a
potential of three \delta-functions, one of them is repulsive and the other two
are attractive, modeling some aspects of the interaction between atoms, and
present an approximate solution for a dilute gas. In this limit, for low energy
states, the results are found to be reduced to the ones of an effective Lieb
Liniger model with an effective \delta-function of strength $c_{eff}$ and the
regime of stability is identified. This may shed light on some aspects of
interacting bosons.
