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We analyze the interaction of lattice vibrations (phonon wave-packets) withan asymmetric kink soliton initially at rest. We employ the $\phi^6$ model inone space and one time dimensions for various lattice spacings and consider twodifferent discretization prescriptions for the field potential that do notgenerate Peierls-Nabarro potentials, i.e. the kink can be placed anywhere alongthe lattice beyond discrete translational invariance. Since the $\phi^6$ modelkink is neither symmetric nor anti-symmetric under spatial reflections wesimulate the cases where the wave-packet approaches the kink from negative orpositive spatial infinity. We extract the energy transmission and reflectioncoefficients as functions of the central frequency of the phonon wave-packetfor the different lattice spacings. For large lattice spacings the wave-packetis always fully reflected while for smaller spacing the amount of reflectionand transmission depends on the central frequency. We also identify scenariosin which the target kink acquires a non-zero velocity from its interaction withthe wave-packet.

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