  Quasinormal modes (QNMs) are essential for understanding the stability and
resonances of open systems, with increasing prominence in black hole physics.
We present here the first study of QNMs of optical potentials. We show that
solitons can support QNMs, deriving a soliton perturbation equation and giving
exact analytical expressions for the QNMs of fiber solitons. We discuss the
boundary conditions in this intrinsically dispersive system and identify novel
signatures of dispersion. From here, we discover a new analogy with black holes
and describe a regime in which the soliton is a robust black hole simulator for
light-ring phenomena. Our results invite a range of applications, from the
description of optical pulse propagation with QNMs to the use of
state-of-the-art technology from fiber optics to address questions in black
hole physics, such as QNM spectral instabilities and the role of nonlinearities
in ringdown.
