  Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in
long cigar-shaped traps are known to be both energetically and dynamically
unstable. They tend to split into single-quantum vortices even in the ultralow
temperature limit with vanishingly weak dissipation, which has also been
confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93,
160406 (2004)] utilizing the so-called topological phase engineering method to
create multiquantum vortices. We study the stability properties of multiquantum
vortices in different trap geometries by solving the Bogoliubov excitation
spectra for such states. We find that there are regions in the trap asymmetry
and condensate interaction strength plane in which the splitting instability of
multiquantum vortices is suppressed, and hence they are dynamically stable. For
example, the doubly quantized vortex can be made dynamically stable even in
spherical traps within a wide range of interaction strength values. We expect
that this suppression of vortex-splitting instability can be experimentally
verified.
