  We consider a scalar field equation in dimension $1+1$ with a positive
external potential having non-degenerate isolated zeros. We construct weakly
interacting pure multi-solitons, that is solutions converging exponentially in
time to a superposition of Lorentz-transformed kinks, in the case of distinct
velocities. We find that these solutions form a $2K$-dimensional smooth
manifold in the space of solutions, where $K$ is the number of the kinks. We
prove that this manifold is invariant under the transformations corresponding
to the invariances of the equation, that is space-time translations and Lorentz
boosts.
