Kink dynamics under odd perturbations for (1+1)-scalar field models with one internal mode

TL;DR

This paper proves the asymptotic stability of kinks in odd symmetric (1+1)-scalar field models with one internal mode, including the $^4$ model, under odd perturbations, using the Fermi golden rule.

Contribution

It establishes the asymptotic stability of kinks in odd symmetric scalar field models with one internal mode, extending previous results to include models like $^4$ with perturbations.

Findings

Asymptotic stability of kinks under odd perturbations proven

Applicable to $^4$ model and similar models with internal modes

Results rely on the Fermi golden rule assumption

Abstract

We consider odd symmetric (1+1)-scalar field models with one internal mode. Under natural and robust assumptions, including the Fermi golden rule, we prove the asymptotic stability of the kink by odd perturbations in the energy space. For example, the result applies to the $\phi^4$ model with odd symmetry and some of its perturbations.