Stability of a BEC with Higher-order Interactions near a Feshbach Resonance

We consider the stability of an ultracold trapped Bose-Einstein condensate near a Feshbach resonance. Using a modified Gross-Pitaevskii equation that includes higher-order terms and a multi-channel model of Feshbach resonances, we find regions where stability can be enhanced or suppressed around experimentally measured resonances. We suggest a number of ways to probe the stability diagram. Using scattering length zero-crossings huge deviations are founds for the critical particle number. Effects are enhanced for narrow resonances or tighter traps. Macroscopic tunneling of the condensate is another possible probe for higher-order interactions, however, to see this requires very narrow resonances or very small particle numbers.