Bose-gas with two- and three-body interactions: evolution of the unstable bubbles

In the mean-field approximation the boson system with two-body attractive and three-body repulsive δ-function interactions reduces to the Ψ3-Ψ5 nonlinear Schroedinger equation: iΨt+ΨXX±Ψ+ΨΨ2-aΨ Ψ4=0, a>0. We have simulated numerically the evolution of the soliton-like ''bubble in the condensate'' solution to this equation, and here the results are reported. The static soliton is found either to decay or to grow without bounds depending on the choice of initial perturbation. As regards the travelling ''bubble'', the growth rate diminishes under velocity increase, and at high speeds the soliton represents a rather long-lived object