  We study the real hyperelliptic solutions of the focusing modified KdV (MKdV)
equation of the genus three. Since the complex hyperelliptic solutions of the
focusing MKdV equation over $\mathbb{C}$ are associated with the real gauged
MKdV equation, we present a novel construction of the real hyperelliptic
solutions of the gauged MKdV equation. When the gauge field is constant, it can
be regarded as the real solution of the focusing MKdV equation, and thus we
also discuss the behavior of the gauge field numerically.
