Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

The critical number of atoms for Bose-Einstein condensates with cylindrically symmetrical traps were calculated. The time evolution of the condensate was also studied at changing ground state. A conjecture on higher-order nonlinear effects was also discussed to determine its signal and strength. The results show that by exchanging frequencies, the geometry favors the condensation of larger number of particles.