  Earlier work has shown that ring dark solitons in two-dimensional
Bose-Einstein condensate are generically unstable. In this work, we propose a
way of stabilizing the ring dark soliton via a radial Gaussian external
potential. We investigate the existence and stability of the ring dark soliton
upon variations of the chemical potential and also of the strength of the
radial potential. Numerical results show that the ring dark soliton can be
stabilized in a suitable interval of external potential strengths and chemical
potentials. We also explore different proposed particle pictures considering
the ring as a moving particle and find, where appropriate, results in very good
qualitative and also reasonable quantitative agreement with the numerical
findings.
