Lattice phonons in the presence of non-linear excitations

We examine the interaction between linear (phonon-like) and non linear (kink, soliton-like) excitations of the classical, discrete, ?⁴ chain in the displacive regime. The discreteness of the lattice manifests itself (a) in the asymptotic phonon phase shift, (b) in partial reflection occurring near the Brillouin zone edge and (c) in the spatial shift suffered by a kink due to its collision with a phonon wavepacket. Our analytical results are confirmed by computer simulations.