A generalized Lieb-Liniger model

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 we 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.