  We study the Korteweg--de Vries equation on a metric star graph and
investigate existence of solitary waves on the metric graph in terms of the
coefficients of the equation on each edge, the coupling condition at the
central vertex of the star and the speeds of the travelling wave. We show that,
with a continuity condition at the vertex, solitary waves can occur exactly
when the parameters are chosen in a fairly special manner. We also consider
coupling conditions beyond continuity.
