Azimuthal splitting instability of attractive vortex states

Determine whether vortex bound states in the two-dimensional system with self-attraction undergo splitting instability, also known as azimuthal modulational instability, under the action of the strong expulsive potential.

Background

The paper reports two-dimensional vortex bound states supported by a steep expulsive potential and notes that self-attractive nonlinearities can produce nontrivial stability phenomena. The authors explicitly identify the possible splitting, or azimuthal modulational, instability of these vortex states as an unresolved question requiring further analysis.

References

There remain open questions concerning this setting, especially as concerns effects of the nonlinearity. In particular, it will be interesting to investigate the interplay of the critical collapse, induced by the cubic or quintic self-attraction in the 1D or 2D cases, respectively, with the strong expulsive potential. Another issue is a possibility of the splitting instability (alias the azimuthal modulational instability) of vortex bound states in the 2D system with self-attraction.

— Quantum-mechanical wave functions in singular potentials: linear and nonlinear states  (2608.20282 - Sakaguchi et al., 20 Aug 2026) in Section Discussion and conclusion