Unstable higher modes of a three-dimensional nonlinear Schrödinger equation

Abstract

Characterized by a central core surrounded by a number of concentric shells, the stability of the higher-bound solitary wave solutions to a three-dimensional nonlinear Schr\"odinger equation with saturating nonlinearity is investigated. A linear stability analysis of spherical harmonic modes reveals these solutions to be transversely unstable. Further, the complicated intermediate patterns observed in numerical simulations are shown to result from a degeneracy in the number of maximally unstable modes, the mode mixture depending on the realization of the destabilizing perturbation.