  This paper concerns classical nonlinear scalar field models on the real line.
If the potential is a symmetric double-well, such a model admits static
solutions called kinks and antikinks, which are perhaps the simplest examples
of topological solitons. We study pure kink-antikink pairs, which are solutions
that converge in one infinite time direction to a superposition of one kink and
one antikink, without radiation. Our main result is a complete classification
of all kink-antikink pairs in the strongly interacting regime, which means the
speeds of the kinks tend asymptotically to zero. We show that up to translation
there is exactly one such solution, and we give a precise description of the
dynamics of the kink separation.
