  We investigate anharmonically coupled high- and low-frequency excitations in
a planar lattice of adsorbed molecules interacting with phonons of a crystal.
Dephasing of high-frequency local vibrations by low-frequency resonance modes
is described in terms of temperature Green's function. The equations obtained
are solved, first, with a small ratio of the anharmonic coupling coefficient
for high- and low-frequency modes to the resonance width, and second, in the
low-temperature limit. High-frequency spectral line positions and widths depend
on dispersion laws and resonance mode lifetimes. It is shown that lateral
interactions of low-frequency modes of adsorbed molecules can lead to a
significant narrowing of high-frequency spectral lines, which is consistent
with experimental data.
