On the localized and delocalized modes in kink-antikink interactions: a toy model

TL;DR

This paper analyzes a scalar field theory with a triple-well potential, providing analytical solutions for localized and delocalized modes, and explores how higher modes influence kink-antikink collision dynamics.

Contribution

It introduces a toy model with an analytically solvable spectrum of modes, enabling detailed study of resonance phenomena in kink interactions.

Findings

Analytical expressions for localized and delocalized modes.

New scenarios of resonance window suppression.

Insights into the role of higher excited modes in kink scattering.

Abstract

This study deals with a piecewise $\phi^2$ scalar field theory in $(1+1)$ dimensions. The scalar field potential is designed with a triple-well shape, engendering kink solutions with asymmetric square-well linearized potentials. Thus, the localized and delocalized modes in this model can be obtained analytically in terms of transcendental equations. This allows us to explore kink-antikink and antikink-kink collisions with any desired number of localized and delocalized modes. We obtain new scenarios of resonance windows suppression, shedding light on the role of higher excited modes in kink scattering.