Kink-antikink scattering in the $\phi^4$ model without static intersoliton forces

TL;DR

This paper explores kink-antikink interactions in the $$ model without static forces, revealing new phenomena like spectral walls, vacuum walls, and higher order spectral walls that influence soliton dynamics and radiation.

Contribution

It introduces the concept of vacuum walls and higher order spectral walls, expanding understanding of soliton interactions in the absence of static inter-soliton forces.

Findings

Spectral walls cause soliton trajectory deformation.

Vacuum walls lead to bouncing behavior of annihilating solitons.

Higher order spectral walls produce intense radiation bursts.

Abstract

Kink-antikink scattering in the $\phi^4$ model is investigated in the limit when the static inter-soliton force vanishes. We observe the formation of spectral walls and, further, identify a new phenomenon, the vacuum wall, whose existence gives rise to a bouncing structure for the annihilating solitons. Furthermore, we discover higher order spectral walls, i.e., spectral walls which form when higher harmonics enter the continuous spectrum. These higher order spectral walls not only deform the soliton trajectories, they also can be observed easily as very intense radiation bursts.