Boundary scattering in the $\phi^{6}$ model

TL;DR

This paper investigates how boundary conditions affect kink and antikink scattering in the non-integrable $$ model on a half-line, revealing dynamics modifications and boundary-dependent outcomes.

Contribution

It provides the first detailed analysis of boundary effects on kink scattering in the $$ model, including stability and topological considerations.

Findings

Boundary conditions significantly influence scattering outcomes.

Increasing boundary parameter $H$ alters defect dynamics.

Multiple possible scattering results depending on initial velocity and boundary.

Abstract

We study the non-integrable $\phi^{6}$ model on the half-line. The model has two topological sectors. We chose solutions from just one topological sector to fix the initial conditions. The scalar field satisfies a Neumann boundary condition $\phi_{x}\left(0,t\right)=H$. We study the scattering of a kink (antikinks) with all possible regular and stable boundaries. When $H=0$ the results are the same observed for scattering for the same model in the full line. With the increasing of $H$, sensible modifications appear in the dynamics with of the defect with several possibilities for the output depending on the initial velocity and the boundary. Our results are confronted with the topological structure and linear stability analysis of kink, antikink and boundary solutions.