Stability of solutions of the nonlinear Schrödinger equation for trapped Bose-condensed atoms with negative scattering lengths

We analyze the time evolution of solutions of nonlinear Schrödinger equations that describe a condensate composed of atoms with negative scattering lengths in a harmonic potential trap. It is theoretically demonstrated that if an initial condensate has negative energies due to negative scattering lengths, then the solutions diverge in a finite time that is determined by the condensate's energy, its initial phase, and the trap parameter.