  We consider a real scalar field equation in dimension 1+1 with an even
positive self-interaction potential having two non-degenerate zeros (vacua) 1
and -1. It is known that such a model admits non-trivial static solutions
called kinks and antikinks. A kink cluster is a solution approaching, for large
positive times, a superposition of alternating kinks and antikinks whose
velocities converge to 0. They can be equivalently characterised as the
solutions of minimal possible energy containing a given number of transitions
between the vacua, or as the solutions whose kinetic energy decays to 0 for
large time. Our main result is a determination of the main-order asymptotic
behaviour of any kink cluster. Moreover, we construct a kink cluster for any
prescribed initial positions of the kinks and antikinks, provided that their
mutual distances are sufficiently large. Finally, we show that kink clusters
are universal profiles for the formation/collapse of multi-kink configurations.
The proofs rely on a reduction, using appropriately chosen modulation
parameters, to an n-body problem with attractive exponential interactions.
