Moduli space with a boundary

TL;DR

This paper explores how the moduli space in solitonic processes can have physically meaningful boundaries, exemplified by kink-antikink annihilation, with solutions exhibiting self-similarity near these boundaries.

Contribution

It demonstrates that boundaries in the moduli space can represent real physical phenomena like soliton annihilation, providing new insights into soliton dynamics.

Findings

Boundaries in moduli space can be physically meaningful.

Kink-antikink annihilation occurs in finite time at the boundary.

Solutions near the boundary show approximate self-similarity.

Abstract

We find that for various solitonic processes the corresponding canonical moduli space can have a boundary which is accessible in a finite time evolution. We show that such a boundary is not a failure of the moduli space approach but has a physical meaning. In our example, it corresponds to the complete annihilation of a colliding kink and antikink after a finite time. We further find that, close to the boundary, the solutions have an approximate self-similar form.