Half-line kink scattering in the φ4 model with Dirichlet boundary conditions

In this work, we investigate the dynamics of a scalar field in the nonintegrable 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.