Resonance phenomena in the $\varphi^8$ kinks scattering

TL;DR

This paper investigates the scattering behavior of $^8$ kinks with power-law asymptotics, identifying critical velocities that determine whether kinks collide, form bound states, or escape, and discovering resonance phenomena called escape windows.

Contribution

It introduces the analysis of $^8$ kink scattering with power-law tails, revealing critical velocities and resonance phenomena not previously studied in this context.

Findings

Identified two critical velocities $v_{cr}^{(1)}$ and $v_{cr}^{(2)}$ for kink collisions.

Discovered resonance phenomena called escape windows within certain velocity ranges.

Demonstrated different collision regimes: repulsion, capture, and escape based on initial velocity.

Abstract

We study the scattering of the $\varphi^8$ kinks with power-law asymptotics. We found two critical values of the initial velocity, $v_{cr}^{(1)}$ and $v_{cr}^{(2)}$, which separate different regimes of the kink-antikink collision. At the initial velocities $v_{in}< v_{cr}^{(1)}$ kinks can not collide due to repulsive force between them. At $v_{in}>v_{cr}^{(2)}$ the kinks escape to spatial infinities after one collision. In the range $v_{cr}^{(1)}\le v_{in}\le v_{cr}^{(2)}$ we observed kinks capture and formation of their bound state. Besides that, at these initial velocities we found resonance phenomena -- escape windows.