D. E. Edmundson, "Unstable halo states of a three-dimensional nonlinear Schroedinger equation," Physical Review A, submitted for publication.

The generalized nonlinear Schroedinger equation (GNLSE) governs the propagation of a 3-dimensional plane-polarized optical envelope in a bulk anomalously dispersive medium possessing an arbitrary intensity-dependent refractive index. The GNLSE supports "halo state" solitary waves comprised of a bright central core surrounded by a number of spherical shells. For a saturable nonlinearity where the zeroth order state is known to be stable, a linear stability analysis of spherical harmonic modes Y(l,m) predicts the upper bound states to be transversely unstable, and, in contrast to the situation in 2-dimensions, families of eigenmodes are found to possess the same growth rate. These predictions are corroborated by direct simulation of the GNLSE.