Solitons in Nonlinear Schrödinger Model and the Collective Ground State of One-Dimensional Delta-Function Gas
We examine one-dimensional Bose gas interacting with delta-function potential using the large-$N$ collective field theory. We show that in the case of attractive potential the uniform ground state is unstable to small perturbations and the instability is cured by formation of a collective ground state, \lq\lq bright soliton'' configuration in corresponding nonlinear Schrödinger field theory.