  The phonon-mode decomposition of the electron-phonon coupling in the
MgB2-like system Li_{1-x}BC is explored using first principles calculations. It
is found that the high temperature superconductivity of such systems results
from extremely strong coupling to only ~2% of the phonon modes. Novel
characteristics of E_2g branches include (1) ``mode lambda'' values of 25 and
greater compared to a mean of $\sim 0.4$ for other modes, (2) a precipitous
Kohn anomaly, and (3) E_2g phonon linewidths within a factor of ~2 of the
frequency itself, indicating impending breakdown of linear electron-phonon
theory. This behavior in borne out by recent inelastic x-ray scattering studies
of MgB2 by Shukla et al.
