  We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole
in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs
curve using the Newton polytope and amoeba. In particular, we show that the
monopole wall splits into subwalls when any of its moduli become large. The
long-distance gauge and Higgs field interactions of these subwalls are abelian,
allowing us to derive an asymptotic metric for the monopole wall moduli space.
