Half-line kink scattering in the $\phi^4$ model with Dirichlet boundary conditions

TL;DR

This paper explores complex boundary-induced phenomena in the nonintegrable $\

Contribution

It introduces a detailed analysis of boundary effects on kink dynamics in the $\

Findings

Discovery of boundary-induced resonant scatterings

Formation of kink-antikink pairs and oscillons

Identification of boundary shape modes

Abstract

In this work, we investigate the dynamics of a scalar field in the nonintegrable $\displaystyle \phi ^{4}$ model, restricted to the half-line. Here we consider singular solutions that interpolate the Dirichlet boundary condition $\phi(x=0,t)=H$ and their scattering with the regular kink solution. The simulations reveal a rich variety of phenomena in the field dynamics, such as the formation of a kink-antikink pair, the generation of oscillons by the boundary perturbations, and the interaction between these objects and the boundary, which causes the emergence of boundary-induced resonant scatterings (for example, oscillon-boundary bound states and kink generation by oscillon-boundary collision) founded into complex fractal structures. Linear perturbation analysis was applied to interpret some aspects of the scattering process. We detected the presence of two shape modes near the boundary. The power spectral density of the scalar field at a fixed point leads to several frequency peaks. Most of them can be explained with some interesting insights for the interaction between the scattering products and the boundary.