Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line

TL;DR

This paper classifies and describes the detailed dynamics of strongly interacting kink-antikink pairs in scalar field models, revealing a unique solution with zero-speed asymptotics and precise separation behavior.

Contribution

It provides a complete classification of all zero-speed, strongly interacting kink-antikink pairs in scalar field models, a novel result in nonlinear soliton dynamics.

Findings

Exactly one such solution exists up to translation.

The dynamics of kink separation are precisely characterized.

The solution converges to a superposition of kink and antikink without radiation.

Abstract

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.