Strongly interacting one-dimensional Bose condensates in power law potentials

We study the interaction effects on the condensates by considering a model of one-dimensional bosons. The power law type external potential allows for the formation of a condensate in these systems. Using a density-functional theory type formalism we obtain an equation describing the condensate wave function in the limit of very strong interactions between the bosons. The properties of the condensate in the model system with strong interactions a re investigated. The equivalence of strongly interacting bosons to noninter acting spinless fermions is demonstrated.