  We analyze the asymptotic performance of nonbinary spatially-coupled
low-density parity-check (SC-LDPC) code ensembles defined over the general
linear group on the binary erasure channel. In particular, we prove threshold
saturation of belief propagation decoding to the so called potential threshold,
using the proof technique based on potential functions introduced by Yedla
\textit{et al.}, assuming that the potential function exists. We rewrite the
density evolution of nonbinary SC-LDPC codes in an equivalent vector recursion
form which is suited for the use of the potential function. We then discuss the
existence of the potential function for the general case of vector recursions
defined by multivariate polynomials, and give a method to construct it. We
define a potential function in a slightly more general form than one by Yedla
\textit{et al.}, in order to make the technique based on potential functions
applicable to the case of nonbinary LDPC codes. We show that the potential
function exists if a solution to a carefully designed system of linear
equations exists. Furthermore, we show numerically the existence of a solution
to the system of linear equations for a large number of nonbinary LDPC code
ensembles, which allows us to define their potential function and thus prove
threshold saturation.
