Phonons scattering off discrete asymmetric solitons in the absence of a Peierls–Nabarro potential

We analyze the interaction of lattice vibrations (phonon wave-packets) with an asymmetric kink soliton initially at rest. We employ the ϕ6 model in one space and one time dimensions for various lattice spacings and consider two different discretization prescriptions for the field potential that do not generate Peierls–Nabarro potentials, i.e. the kink can be placed anywhere along the lattice beyond discrete translational invariance. Since the ϕ6 model kink is neither symmetric nor anti-symmetric under spatial reflections, we simulate the cases where the wave-packet approaches the kink from negative or positive spatial infinity. We extract the energy transmission and reflection coefficients as functions of the central frequency of the phonon wave-packet for the different lattice spacings. For large lattice spacings, the wave-packet is always fully reflected, while for smaller spacings the amount of reflection and transmission depends on the central frequency. We also identify scenarios in which the target kink acquires a non-zero velocity from its interaction with the wave-packet.