  We consider the semilinear wave equation with power nonlinearity in one space
dimension. Given a blow-up solution with a characteristic point, we refine the
blow-up behavior first derived by Merle and Zaag. We also refine the geometry
of the blow-up set near a characteristic point, and show that except may be for
one exceptional situation, it is never symmetric with the respect to the
characteristic point. Then, we show that all blow-up modalities predicted by
those authors do occur. More precisely, given any integer $k\ge 2$ and $\zeta_0
\in \m R$, we construct a blow-up solution with a characteristic point $a$,
such that the asymptotic behavior of the solution near $(a,T(a))$ shows a
decoupled sum of $k$ solitons with alternate signs, whose centers (in the
hyperbolic geometry) have $\zeta_0$ as a center of mass, for all times.
